15 January 2013 8:29:27.671 AM TEST_ZERO_PRB FORTRAN77 version Test the TEST_ZERO library. Function value tolerance = 0.100000E-05 Root absolute tolerance = 0.100000E-05 Root relative tolerance = 0.100000E-05 Maximum number of steps = 25 Number of problems is 19 Problem number 1 F(X) = SIN(X) - 0.5 * X We seek roots between -1000.00 and 1000.00 Number of known roots = 3 Tabulated solutions: X F(X) -1.8954943 0.0000000 0.0000000 0.0000000 1.8954943 0.0000000 Number of starting points = 2 I XSTART(I), F(XSTART(I)) 1 1.5707963 0.21460184 2 3.1415927 -1.5707963 BISECTION Step XA XB F(XA) F(XB) 0 3.1415927 1.5707963 -1.57080 0.214602 1 2.3561945 1.5707963 -0.470990 0.214602 2 1.9634954 1.5707963 -0.578682E-01 0.214602 3 1.9634954 1.7671459 -0.578682E-01 0.972123E-01 4 1.9634954 1.8653206 -0.578682E-01 0.242800E-01 5 1.9144080 1.8653206 -0.156599E-01 0.242800E-01 6 1.9144080 1.8898643 -0.156599E-01 0.459602E-02 7 1.9021362 1.8898643 -0.546076E-02 0.459602E-02 8 1.8960003 1.8898643 -0.414536E-03 0.459602E-02 9 1.8960003 1.8929323 -0.414536E-03 0.209520E-02 10 1.8960003 1.8944663 -0.414536E-03 0.841449E-03 11 1.8960003 1.8952333 -0.414536E-03 0.213736E-03 12 1.8956168 1.8952333 -0.100330E-03 0.213736E-03 13 1.8956168 1.8954250 -0.100330E-03 0.567200E-04 14 1.8955209 1.8954250 -0.218009E-04 0.567200E-04 15 1.8955209 1.8954729 -0.218009E-04 0.174606E-04 16 1.8954969 1.8954729 -0.216988E-05 0.174606E-04 17 1.8954969 1.8954849 -0.216988E-05 0.764543E-05 18 1.8954969 1.8954909 -0.216988E-05 0.273780E-05 19 1.8954969 1.8954939 -0.216988E-05 0.283963E-06 Function small enough for convergence. BRENT Step XA XB F(XA) F(XB) 0 3.1415927 1.5707963 -1.57080 0.214602 1 1.7596034 3.1415927 0.102427 -1.57080 2 1.9214503 1.7596034 -0.215768E-01 0.102427 3 1.8932887 1.9214503 0.180410E-02 -0.215768E-01 4 1.8954617 1.9214503 0.266883E-04 -0.215768E-01 5 1.8954943 1.8954617 -0.109785E-08 0.266883E-04 Function small enough for convergence. NEWTON Step X F(X) FP(X) 0 1.5707963 0.214602 -0.500000 1 2.0000000 -0.907026E-01 -0.916147 2 1.9009956 -0.452004E-02 -0.824232 3 1.8955116 -0.142334E-04 -0.819039 4 1.8954943 -0.143110E-09 -0.819023 The function norm is small enough for convergence. NEWTON Step X F(X) FP(X) 0 3.1415927 -1.57080 -1.50000 1 2.0943951 -0.181172 -1.00000 2 1.9132230 -0.146688E-01 -0.835774 3 1.8956718 -0.145379E-03 -0.819191 4 1.8954943 -0.149238E-07 -0.819023 The function norm is small enough for convergence. REGULA FALSI Step XA XB F(XA) F(XB) 0 3.1415927 1.5707963 -1.57080 0.214602 1 3.1415927 1.7596034 -1.57080 0.102427 2 3.1415927 1.8442025 -1.57080 0.407555E-01 3 3.1415927 1.8770130 -1.57080 0.149744E-01 4 3.1415927 1.8889544 -1.57080 0.533603E-02 5 3.1415927 1.8931952 -1.57080 0.188047E-02 6 3.1415927 1.8946879 -1.57080 0.660091E-03 7 3.1415927 1.8952117 -1.57080 0.231388E-03 8 3.1415927 1.8953953 -1.57080 0.810710E-04 9 3.1415927 1.8954596 -1.57080 0.283999E-04 10 3.1415927 1.8954821 -1.57080 0.994815E-05 11 3.1415927 1.8954900 -1.57080 0.348465E-05 12 3.1415927 1.8954928 -1.57080 0.122060E-05 13 3.1415927 1.8954937 -1.57080 0.427547E-06 Function small enough for convergence. SECANT Step X F(X) -1 1.5707963 0.214602 0 3.1415927 -1.57080 1 1.7596034 0.102427 2 1.8442025 0.407555E-01 3 1.9001096 -0.379015E-02 4 1.8953528 0.115882E-03 5 1.8954939 0.308518E-06 Function small enough for convergence. Problem number 2 F(X) = 2 * X - EXP ( - X ) We seek roots between -10.0000 and 100.000 Number of known roots = 1 Tabulated solutions: X F(X) 0.35173371 0.0000000 Number of starting points = 4 I XSTART(I), F(XSTART(I)) 1 0.0000000 -1.0000000 2 1.0000000 1.6321206 3 -5.0000000 -158.41316 4 10.000000 19.999955 BISECTION Step XA XB F(XA) F(XB) 0 0.0000000 1.0000000 -1.00000 1.63212 1 0.0000000 0.50000000 -1.00000 0.393469 2 0.25000000 0.50000000 -0.278801 0.393469 3 0.25000000 0.37500000 -0.278801 0.627107E-01 4 0.31250000 0.37500000 -0.106616 0.627107E-01 5 0.34375000 0.37500000 -0.216062E-01 0.627107E-01 6 0.34375000 0.35937500 -0.216062E-01 0.206375E-01 7 0.35156250 0.35937500 -0.462874E-03 0.206375E-01 8 0.35156250 0.35546875 -0.462874E-03 0.100927E-01 9 0.35156250 0.35351563 -0.462874E-03 0.481623E-02 10 0.35156250 0.35253906 -0.462874E-03 0.217701E-02 11 0.35156250 0.35205078 -0.462874E-03 0.857153E-03 12 0.35156250 0.35180664 -0.462874E-03 0.197160E-03 13 0.35168457 0.35180664 -0.132852E-03 0.197160E-03 14 0.35168457 0.35174561 -0.132852E-03 0.321556E-04 15 0.35171509 0.35174561 -0.503478E-04 0.321556E-04 16 0.35173035 0.35174561 -0.909601E-05 0.321556E-04 17 0.35173035 0.35173798 -0.909601E-05 0.115298E-04 18 0.35173035 0.35173416 -0.909601E-05 0.121691E-05 19 0.35173225 0.35173416 -0.393955E-05 0.121691E-05 20 0.35173321 0.35173416 -0.136132E-05 0.121691E-05 Interval small enough for convergence. BRENT Step XA XB F(XA) F(XB) 0 1.0000000 0.0000000 1.63212 -1.00000 1 0.37992181 0.0000000 0.759287E-01 -1.00000 2 0.35311057 0.0000000 0.372163E-02 -1.00000 3 0.35173382 0.0000000 0.282665E-06 -1.00000 Function small enough for convergence. MULLER Step XA XB XC F(XA) F(XB) F(XC) 0 0.00000 1.00000 -5.00000 -1.00000 1.63212 -158.413 1 0.00000 1.00000 0.148686 -1.00000 1.63212 -0.564469 2 0.00000 0.148686 0.349768 -1.00000 -0.564469 -0.531486E-02 3 0.148686 0.349768 0.351741 -0.564469 -0.531486E-02 0.190258E-04 4 0.349768 0.351741 0.351734 -0.531486E-02 0.190258E-04 -0.346878E-09 Function small enough for convergence. NEWTON Step X F(X) FP(X) 0 0.0000000 -1.00000 3.00000 1 0.33333333 -0.498646E-01 2.71653 2 0.35168933 -0.119980E-03 2.70350 3 0.35173371 -0.692772E-09 2.70347 The function norm is small enough for convergence. NEWTON Step X F(X) FP(X) 0 1.0000000 1.63212 2.36788 1 0.31072481 -0.111466 2.73292 2 0.35151126 -0.601411E-03 2.70362 3 0.35173370 -0.174072E-07 2.70347 The function norm is small enough for convergence. NEWTON Step X F(X) FP(X) 0 -5.0000000 -158.413 150.413 1 -3.9468132 -59.6637 53.7701 2 -2.8372053 -22.7424 19.0680 3 -1.6445050 -8.46746 7.17845 4 -0.46493824 -2.52179 3.59192 5 0.23713621 -0.314611 2.78888 6 0.34994529 -0.483608E-02 2.70473 7 0.35173329 -0.112583E-05 2.70347 8 0.35173371 -0.609512E-13 2.70347 The function norm is small enough for convergence. NEWTON Step X F(X) FP(X) 0 10.000000 20.0000 2.00005 1 0.24969395E-03 -0.999251 2.99975 2 0.33336107 -0.497893E-01 2.71651 3 0.35168947 -0.119617E-03 2.70350 4 0.35173371 -0.688590E-09 2.70347 The function norm is small enough for convergence. REGULA FALSI Step XA XB F(XA) F(XB) 0 0.0000000 1.0000000 -1.00000 1.63212 1 0.0000000 0.37992181 -1.00000 0.759287E-01 2 0.0000000 0.35311057 -1.00000 0.372163E-02 3 0.0000000 0.35180130 -1.00000 0.182714E-03 4 0.0000000 0.35173703 -1.00000 0.897113E-05 5 0.0000000 0.35173387 -1.00000 0.440477E-06 Function small enough for convergence. SECANT Step X F(X) -1 0.0000000 -1.00000 0 1.0000000 1.63212 1 0.37992181 0.759287E-01 2 0.34966734 -0.558786E-02 3 0.35174125 0.203789E-04 4 0.35173371 0.548104E-08 Function small enough for convergence. SECANT Step X F(X) -1 1.0000000 1.63212 0 -5.0000000 -158.413 1 0.93881279 1.48653 2 0.88360165 1.35391 3 0.31996257 -0.862511E-01 4 0.35371881 0.536527E-02 5 0.35174197 0.223180E-04 6 0.35173371 -0.576176E-08 Function small enough for convergence. SECANT Step X F(X) -1 -5.0000000 -158.413 0 10.000000 20.0000 1 8.3185131 16.6368 2 0.61308886E-03 -0.998161 3 0.47141714 0.318717 4 0.35747090 0.154987E-01 5 0.35164664 -0.235410E-03 6 0.35173378 0.175515E-06 Function small enough for convergence. Problem number 3 F(X) = X * EXP ( - X ) We seek roots between -10.0000 and 100.000 Number of known roots = 1 Tabulated solutions: X F(X) 0.0000000 0.0000000 Number of starting points = 3 I XSTART(I), F(XSTART(I)) 1 -1.0000000 -2.7182818 2 0.50000000 0.30326533 3 2.0000000 0.27067057 BISECTION Step XA XB F(XA) F(XB) 0 -1.0000000 0.50000000 -2.71828 0.303265 1 -0.25000000 0.50000000 -0.321006 0.303265 2 -0.25000000 0.12500000 -0.321006 0.110312 3 -0.62500000E-01 0.12500000 -0.665309E-01 0.110312 4 -0.62500000E-01 0.31250000E-01 -0.665309E-01 0.302885E-01 5 -0.15625000E-01 0.31250000E-01 -0.158711E-01 0.302885E-01 6 -0.15625000E-01 0.78125000E-02 -0.158711E-01 0.775170E-02 7 -0.39062500E-02 0.78125000E-02 -0.392154E-02 0.775170E-02 8 -0.39062500E-02 0.19531250E-02 -0.392154E-02 0.194931E-02 9 -0.97656250E-03 0.19531250E-02 -0.977517E-03 0.194931E-02 10 -0.97656250E-03 0.48828125E-03 -0.977517E-03 0.488043E-03 11 -0.24414063E-03 0.48828125E-03 -0.244200E-03 0.488043E-03 12 -0.24414063E-03 0.12207031E-03 -0.244200E-03 0.122055E-03 13 -0.61035156E-04 0.12207031E-03 -0.610389E-04 0.122055E-03 14 -0.61035156E-04 0.30517578E-04 -0.610389E-04 0.305166E-04 15 -0.15258789E-04 0.30517578E-04 -0.152590E-04 0.305166E-04 16 -0.15258789E-04 0.76293945E-05 -0.152590E-04 0.762934E-05 17 -0.38146973E-05 0.76293945E-05 -0.381471E-05 0.762934E-05 18 -0.38146973E-05 0.19073486E-05 -0.381471E-05 0.190734E-05 19 -0.95367432E-06 0.19073486E-05 -0.953675E-06 0.190734E-05 Function small enough for convergence. BRENT Step XA XB F(XA) F(XB) 0 0.50000000 -1.0000000 0.303265 -2.71828 1 0.34944865 -1.0000000 0.246388 -2.71828 2 -0.24852793 0.34944865 -0.318647 0.246388 3 0.88696039E-01 -0.24852793 0.811678E-01 -0.318647 4 -0.13397964E-01 0.88696039E-01 -0.135787E-01 0.811678E-01 5 0.12337235E-02 -0.13397964E-01 0.123220E-02 -0.135787E-01 6 0.16429166E-04 -0.13397964E-01 0.164289E-04 -0.135787E-01 7 -0.40352160E-09 0.16429166E-04 -0.403522E-09 0.164289E-04 Function small enough for convergence. MULLER Step XA XB XC F(XA) F(XB) F(XC) 0 -1.00000 0.500000 2.00000 -2.71828 0.303265 0.270671 1 0.500000 2.00000 2.22675 0.303265 0.270671 0.240218 2 2.00000 2.22675 3.31767 0.270671 0.240218 0.120223 3 2.22675 3.31767 5.99306 0.240218 0.120223 0.149587E-01 4 3.31767 2.22675 3.23322 0.120223 0.240218 0.127487 5 3.31767 3.23322 6.12976 0.120223 0.127487 0.133451E-01 6 3.23322 3.31767 3.02704 0.127487 0.120223 0.146687 7 3.31767 3.23322 6.01563 0.120223 0.127487 0.146800E-01 8 3.23322 3.31767 1.39385 0.127487 0.120223 0.345839 9 3.31767 3.23322 6.00594 0.120223 0.127487 0.147991E-01 10 3.23322 3.31767 1.19875 0.127487 0.120223 0.361508 11 3.31767 3.23322 5.50978 0.120223 0.127487 0.222981E-01 12 3.31767 5.50978 14.6826 0.120223 0.222981E-01 0.616932E-05 13 5.50978 14.6826 14.6824 0.222981E-01 0.616932E-05 0.617044E-05 14 14.6826 14.6824 16.8097 0.616932E-05 0.617044E-05 0.841781E-06 Function small enough for convergence. NEWTON Step X F(X) FP(X) 0 -1.0000000 -2.71828 5.43656 1 -0.50000000 -0.824361 2.47308 2 -0.16666667 -0.196893 1.37825 3 -0.23809524E-01 -0.243832E-01 1.04848 4 -0.55370986E-03 -0.554017E-03 1.00111 5 -0.30642493E-06 -0.306425E-06 1.00000 The function norm is small enough for convergence. NEWTON Step X F(X) FP(X) 0 0.50000000 0.303265 0.303265 1 -0.50000000 -0.824361 2.47308 2 -0.16666667 -0.196893 1.37825 3 -0.23809524E-01 -0.243832E-01 1.04848 4 -0.55370986E-03 -0.554017E-03 1.00111 5 -0.30642493E-06 -0.306425E-06 1.00000 The function norm is small enough for convergence. NEWTON Step X F(X) FP(X) 0 2.0000000 0.270671 -0.135335 1 4.0000000 0.732626E-01 -0.549469E-01 2 5.3333333 0.257491E-01 -0.209211E-01 3 6.5641026 0.925597E-02 -0.784588E-02 4 7.7438261 0.335625E-02 -0.292284E-02 5 8.8921098 0.122239E-02 -0.108492E-02 6 10.018819 0.446374E-03 -0.401820E-03 7 11.129698 0.163274E-03 -0.148604E-03 8 12.228418 0.597910E-04 -0.549015E-04 9 13.317477 0.219137E-04 -0.202682E-04 10 14.398663 0.803642E-05 -0.747828E-05 11 15.473297 0.294860E-05 -0.275804E-05 12 16.542390 0.108226E-05 -0.101683E-05 13 17.606730 0.397350E-06 -0.374782E-06 The function norm is small enough for convergence. REGULA FALSI Step XA XB F(XA) F(XB) 0 -1.0000000 0.50000000 -2.71828 0.303265 1 -1.0000000 0.34944865 -2.71828 0.246388 2 -1.0000000 0.23729853 -2.71828 0.187171 3 -1.0000000 0.15759118 -2.71828 0.134614 4 -1.0000000 0.10297011 -2.71828 0.928949E-01 5 -1.0000000 0.66522640E-01 -2.71828 0.622414E-01 6 -1.0000000 0.42648782E-01 -2.71828 0.408681E-01 7 -1.0000000 0.27205228E-01 -2.71828 0.264751E-01 8 -1.0000000 0.17297123E-01 -2.71828 0.170005E-01 9 -1.0000000 0.10974351E-01 -2.71828 0.108546E-01 10 -1.0000000 0.69534107E-02 -2.71828 0.690523E-02 11 -1.0000000 0.44019369E-02 -2.71828 0.438260E-02 12 -1.0000000 0.27851771E-02 -2.71828 0.277743E-02 13 -1.0000000 0.17616175E-02 -2.71828 0.175852E-02 14 -1.0000000 0.11139746E-02 -2.71828 0.111273E-02 15 -1.0000000 0.70433420E-03 -2.71828 0.703838E-03 16 -1.0000000 0.44529127E-03 -2.71828 0.445093E-03 17 -1.0000000 0.28150460E-03 -2.71828 0.281425E-03 18 -1.0000000 0.17795557E-03 -2.71828 0.177924E-03 19 -1.0000000 0.11249366E-03 -2.71828 0.112481E-03 20 -1.0000000 0.71111268E-04 -2.71828 0.711062E-04 21 -1.0000000 0.44951579E-04 -2.71828 0.449496E-04 22 -1.0000000 0.28415090E-04 -2.71828 0.284143E-04 23 -1.0000000 0.17961872E-04 -2.71828 0.179615E-04 24 -1.0000000 0.11354112E-04 -2.71828 0.113540E-04 25 -1.0000000 0.71771853E-05 -2.71828 0.717713E-05 Took maximum number of steps without convergence. SECANT Step X F(X) -1 -1.0000000 -2.71828 0 0.50000000 0.303265 1 0.34944865 0.246388 2 -0.30272920 -0.409758 3 0.10455083 0.941720E-01 4 0.28440401E-01 0.276429E-01 5 -0.31836281E-02 -0.319378E-02 6 0.91693964E-04 0.916856E-04 7 0.29146862E-06 0.291469E-06 Function small enough for convergence. SECANT Step X F(X) -1 0.50000000 0.303265 0 2.0000000 0.270671 1 14.456168 0.761762E-05 2 14.456519 0.761513E-05 3 15.530658 0.279454E-05 4 16.153347 0.155938E-05 5 16.939490 0.745030E-06 Function small enough for convergence. Problem number 4 F(X) = EXP ( X ) - 1 / ( 10 * X )^2 We seek roots between 0.100000E-04 and 20.0000 Number of known roots = 1 Tabulated solutions: X F(X) 0.95344617E-01 -0.22204460E-15 Number of starting points = 2 I XSTART(I), F(XSTART(I)) 1 0.30000000E-01 -10.080657 2 1.0000000 2.7082818 BISECTION Step XA XB F(XA) F(XB) 0 0.30000000E-01 1.0000000 -10.0807 2.70828 1 0.30000000E-01 0.51500000 -10.0807 1.63593 2 0.30000000E-01 0.27250000 -10.0807 1.17857 3 0.30000000E-01 0.15125000 -10.0807 0.726159 4 0.90625000E-01 0.15125000 -0.122740 0.726159 5 0.90625000E-01 0.12093750 -0.122740 0.444835 6 0.90625000E-01 0.10578125 -0.122740 0.217898 7 0.90625000E-01 0.98203125E-01 -0.122740 0.662570E-01 8 0.94414063E-01 0.98203125E-01 -0.228142E-01 0.662570E-01 9 0.94414063E-01 0.96308594E-01 -0.228142E-01 0.229718E-01 10 0.94414063E-01 0.95361328E-01 -0.228142E-01 0.403886E-03 11 0.94887695E-01 0.95361328E-01 -0.111223E-01 0.403886E-03 12 0.95124512E-01 0.95361328E-01 -0.533867E-02 0.403886E-03 13 0.95242920E-01 0.95361328E-01 -0.246229E-02 0.403886E-03 14 0.95302124E-01 0.95361328E-01 -0.102793E-02 0.403886E-03 15 0.95331726E-01 0.95361328E-01 -0.311704E-03 0.403886E-03 16 0.95331726E-01 0.95346527E-01 -0.311704E-03 0.461705E-04 17 0.95339127E-01 0.95346527E-01 -0.132747E-03 0.461705E-04 18 0.95342827E-01 0.95346527E-01 -0.432831E-04 0.461705E-04 19 0.95342827E-01 0.95344677E-01 -0.432831E-04 0.144497E-05 20 0.95343752E-01 0.95344677E-01 -0.209187E-04 0.144497E-05 Interval small enough for convergence. BRENT Step XA XB F(XA) F(XB) 0 1.0000000 0.30000000E-01 2.70828 -10.0807 1 0.79458550 0.30000000E-01 2.19768 -10.0807 2 0.41229275 0.30000000E-01 1.45145 -10.0807 3 0.22114638 0.30000000E-01 1.04303 -10.0807 4 0.12557319 0.30000000E-01 0.499627 -10.0807 5 0.77786594E-01 0.12557319 -0.571795 0.499627 6 0.10328926 0.77786594E-01 0.171488 -0.571795 7 0.94330376E-01 0.10328926 -0.248975E-01 0.171488 8 0.95466172E-01 0.94330376E-01 0.293325E-02 -0.248975E-01 9 0.95346464E-01 0.94330376E-01 0.446469E-04 -0.248975E-01 10 0.95344617E-01 0.95346464E-01 -0.131765E-08 0.446469E-04 Function small enough for convergence. NEWTON Step X F(X) FP(X) 0 0.30000000E-01 -10.0807 741.771 1 0.43589981E-01 -4.21836 242.518 2 0.60983985E-01 -1.62598 89.2454 3 0.79203176E-01 -0.511673 41.3358 4 0.91581626E-01 -0.963876E-01 27.1337 5 0.95133941E-01 -0.510924E-02 24.3284 6 0.95343952E-01 -0.160817E-04 24.1755 7 0.95344617E-01 -0.160399E-09 24.1750 The function norm is small enough for convergence. NEWTON Step X F(X) FP(X) 0 1.0000000 2.70828 2.73828 1 0.10955775E-01 -82.3022 15210.0 2 0.16366828E-01 -36.3146 4562.82 3 0.24325640E-01 -15.8748 1390.46 4 0.35742599E-01 -6.79119 439.034 5 0.51211099E-01 -2.76050 149.967 6 0.69618438E-01 -0.991149 60.3451 7 0.86043110E-01 -0.260874 32.4864 8 0.94073378E-01 -0.313286E-01 25.1218 9 0.95320448E-01 -0.584500E-03 24.1926 10 0.95344608E-01 -0.211728E-06 24.1750 The function norm is small enough for convergence. REGULA FALSI Step XA XB F(XA) F(XB) 0 0.30000000E-01 1.0000000 -10.0807 2.70828 1 0.30000000E-01 0.79458550 -10.0807 2.19768 2 0.30000000E-01 0.65773332 -10.0807 1.90730 3 0.30000000E-01 0.55786026 -10.0807 1.71480 4 0.30000000E-01 0.48112108 -10.0807 1.57469 5 0.30000000E-01 0.42017270 -10.0807 1.46558 6 0.30000000E-01 0.37064748 -10.0807 1.37588 7 0.30000000E-01 0.32973717 -10.0807 1.29863 8 0.30000000E-01 0.29553052 -10.0807 1.22934 9 0.30000000E-01 0.26666864 -10.0807 1.16498 10 0.30000000E-01 0.24215111 -10.0807 1.10345 11 0.30000000E-01 0.22121985 -10.0807 1.04326 12 0.30000000E-01 0.20328626 -10.0807 0.983441 13 0.30000000E-01 0.18788358 -10.0807 0.923409 14 0.30000000E-01 0.17463474 -10.0807 0.862913 15 0.30000000E-01 0.16323012 -10.0807 0.801990 16 0.30000000E-01 0.15341181 -10.0807 0.740909 17 0.30000000E-01 0.14496230 -10.0807 0.680124 18 0.30000000E-01 0.13769623 -10.0807 0.620208 19 0.30000000E-01 0.13145430 -10.0807 0.561790 20 0.30000000E-01 0.12609876 -10.0807 0.505499 21 0.30000000E-01 0.12150996 -10.0807 0.451908 22 0.30000000E-01 0.11758365 -10.0807 0.401496 23 0.30000000E-01 0.11422895 -10.0807 0.354623 24 0.30000000E-01 0.11136659 -10.0807 0.311517 25 0.30000000E-01 0.10892754 -10.0807 0.272281 Took maximum number of steps without convergence. SECANT Step X F(X) -1 0.30000000E-01 -10.0807 0 1.0000000 2.70828 1 0.79458550 2.19768 2 -0.89548395E-01 -0.332707 Iterate has left the region [XMIN,XMAX]. Problem number 5 F(X) = ( X + 3 ) * ( X - 1 )^2 We seek roots between -1000.00 and 1000.00 Number of known roots = 3 Tabulated solutions: X F(X) -3.0000000 0.0000000 1.0000000 0.0000000 1.0000000 0.0000000 Number of starting points = 2 I XSTART(I), F(XSTART(I)) 1 2.0000000 5.0000000 2 -5.0000000 -72.000000 BISECTION Step XA XB F(XA) F(XB) 0 -5.0000000 2.0000000 -72.0000 5.00000 1 -5.0000000 -1.5000000 -72.0000 9.37500 2 -3.2500000 -1.5000000 -4.51563 9.37500 3 -3.2500000 -2.3750000 -4.51563 7.11914 4 -3.2500000 -2.8125000 -4.51563 2.72534 5 -3.0312500 -2.8125000 -0.507843 2.72534 6 -3.0312500 -2.9218750 -0.507843 1.20165 7 -3.0312500 -2.9765625 -0.507843 0.370618 8 -3.0039063 -2.9765625 -0.626221E-01 0.370618 9 -3.0039063 -2.9902344 -0.626221E-01 0.155488 10 -3.0039063 -2.9970703 -0.626221E-01 0.468064E-01 11 -3.0004883 -2.9970703 -0.781441E-02 0.468064E-01 12 -3.0004883 -2.9987793 -0.781441E-02 0.195193E-01 13 -3.0004883 -2.9996338 -0.781441E-02 0.585830E-02 14 -3.0000610 -2.9996338 -0.976592E-03 0.585830E-02 15 -3.0000610 -2.9998474 -0.976592E-03 0.244122E-02 16 -3.0000610 -2.9999542 -0.976592E-03 0.732405E-03 17 -3.0000076 -2.9999542 -0.122071E-03 0.732405E-03 18 -3.0000076 -2.9999809 -0.122071E-03 0.305173E-03 19 -3.0000076 -2.9999943 -0.122071E-03 0.915525E-04 20 -3.0000010 -2.9999943 -0.152588E-04 0.915525E-04 21 -3.0000010 -2.9999976 -0.152588E-04 0.381469E-04 22 -3.0000010 -2.9999993 -0.152588E-04 0.114441E-04 23 -3.0000001 -2.9999993 -0.190735E-05 0.114441E-04 Interval small enough for convergence. BRENT Step XA XB F(XA) F(XB) 0 -5.0000000 2.0000000 -72.0000 5.00000 1 1.5454545 -5.0000000 1.35237 -72.0000 2 1.3800380 -5.0000000 0.632604 -72.0000 3 1.2363083 -5.0000000 0.236562 -72.0000 4 -1.8818459 -5.0000000 9.28631 -72.0000 5 -3.4409229 -1.8818459 -8.69579 9.28631 6 -2.6869838 -3.4409229 4.25510 -8.69579 7 -2.9346952 -3.4409229 1.01104 -8.69579 8 -3.0038554 -2.9346952 -0.618060E-01 1.01104 9 -2.9998712 -3.0038554 0.206145E-02 -0.618060E-01 10 -2.9999998 -3.0038554 0.396860E-05 -0.618060E-01 11 -3.0000063 -2.9999998 -0.100032E-03 0.396860E-05 Interval small enough for convergence. NEWTON Step X F(X) FP(X) 0 2.0000000 5.00000 11.0000 1 1.5454545 1.35237 5.25620 2 1.2881647 0.356084 2.55443 3 1.1487661 0.918178E-01 1.25652 4 1.0756932 0.233515E-01 0.622734 5 1.0381948 0.589109E-02 0.309935 6 1.0191873 0.147967E-02 0.154603 7 1.0096165 0.370797E-03 0.772094E-01 8 1.0048140 0.928101E-04 0.385816E-01 9 1.0024084 0.232165E-04 0.192850E-01 10 1.0012046 0.580586E-05 0.964104E-02 11 1.0006024 0.145168E-05 0.482016E-02 12 1.0003012 0.362948E-06 0.240999E-02 The function norm is small enough for convergence. NEWTON Step X F(X) FP(X) 0 -5.0000000 -72.0000 60.0000 1 -3.8000000 -18.4320 30.7200 2 -3.2000000 -3.52800 19.3200 3 -3.0173913 -0.280686 16.2792 4 -3.0001493 -0.238868E-02 16.0024 5 -3.0000000 -0.178260E-06 16.0000 The function norm is small enough for convergence. REGULA FALSI Step XA XB F(XA) F(XB) 0 -5.0000000 2.0000000 -72.0000 5.00000 1 -5.0000000 1.5454545 -72.0000 1.35237 2 -5.0000000 1.4247788 -72.0000 0.798394 3 -5.0000000 1.3543170 -72.0000 0.546643 4 -5.0000000 1.3064368 -72.0000 0.404390 5 -5.0000000 1.2712144 -72.0000 0.314179 6 -5.0000000 1.2439683 -72.0000 0.252603 7 -5.0000000 1.2221387 -72.0000 0.208344 8 -5.0000000 1.2041858 -72.0000 0.175280 9 -5.0000000 1.1891187 -72.0000 0.149828 10 -5.0000000 1.1762663 -72.0000 0.129756 11 -5.0000000 1.1651557 -72.0000 0.113610 12 -5.0000000 1.1554429 -72.0000 0.100406 13 -5.0000000 1.1468709 -72.0000 0.894524E-01 14 -5.0000000 1.1392435 -72.0000 0.802548E-01 15 -5.0000000 1.1324080 -72.0000 0.724489E-01 16 -5.0000000 1.1262436 -72.0000 0.657618E-01 17 -5.0000000 1.1206533 -72.0000 0.599852E-01 18 -5.0000000 1.1155582 -72.0000 0.549579E-01 19 -5.0000000 1.1108937 -72.0000 0.505534E-01 20 -5.0000000 1.1066061 -72.0000 0.466710E-01 21 -5.0000000 1.1026503 -72.0000 0.432300E-01 22 -5.0000000 1.0989884 -72.0000 0.401648E-01 23 -5.0000000 1.0955880 -72.0000 0.374217E-01 24 -5.0000000 1.0924215 -72.0000 0.349564E-01 25 -5.0000000 1.0894650 -72.0000 0.327320E-01 Took maximum number of steps without convergence. SECANT Step X F(X) -1 2.0000000 5.00000 0 -5.0000000 -72.0000 1 1.5454545 1.35237 2 1.4247788 0.798394 3 1.2508591 0.267508 4 1.1632228 0.110915 5 1.1011496 0.419598E-01 6 1.0633776 0.163215E-01 7 1.0393319 0.624883E-02 8 1.0244144 0.239881E-02 9 1.0151199 0.917903E-03 10 1.0093589 0.351178E-03 11 1.0057891 0.134247E-03 12 1.0035799 0.513077E-04 13 1.0022132 0.196043E-04 14 1.0013681 0.748977E-05 15 1.0008457 0.286121E-05 16 1.0005227 0.109297E-05 17 1.0003231 0.417499E-06 Function small enough for convergence. Problem number 6 F(X) = EXP(X) - 2 - 1 / ( 10 * X )^2 - 2 / ( 100 * X )^3 We seek roots between 0.100000E-04 and 20.0000 Number of known roots = 1 Tabulated solutions: X F(X) 0.70320484 0.17390095E-15 Number of starting points = 2 I XSTART(I), F(XSTART(I)) 1 0.20000000E-03 -0.99979998 2 2.0000000 5.3865563 BISECTION Step XA XB F(XA) F(XB) 0 0.20000000E-03 2.0000000 -0.999800 5.38656 1 0.20000000E-03 1.0001000 -0.999800 0.708558 2 0.50015000 1.0001000 -0.390991 0.708558 3 0.50015000 0.75012500 -0.390991 0.994975E-01 4 0.62513750 0.75012500 -0.157078 0.994975E-01 5 0.68763125 0.75012500 -0.321443E-01 0.994975E-01 6 0.68763125 0.71887812 -0.321443E-01 0.327847E-01 7 0.68763125 0.70325469 -0.321443E-01 0.103570E-03 8 0.69544297 0.70325469 -0.160737E-01 0.103570E-03 9 0.69934883 0.70325469 -0.799850E-02 0.103570E-03 10 0.70130176 0.70325469 -0.395084E-02 0.103570E-03 11 0.70227822 0.70325469 -0.192448E-02 0.103570E-03 12 0.70276646 0.70325469 -0.910666E-03 0.103570E-03 13 0.70301057 0.70325469 -0.403601E-03 0.103570E-03 14 0.70313263 0.70325469 -0.150029E-03 0.103570E-03 15 0.70319366 0.70325469 -0.232326E-04 0.103570E-03 16 0.70319366 0.70322417 -0.232326E-04 0.401678E-04 17 0.70319366 0.70320892 -0.232326E-04 0.846740E-05 18 0.70320129 0.70320892 -0.738267E-05 0.846740E-05 19 0.70320129 0.70320510 -0.738267E-05 0.542347E-06 Function small enough for convergence. BRENT Step XA XB F(XA) F(XB) 0 2.0000000 0.20000000E-03 5.38656 -0.999800 1 0.31327367 2.0000000 -0.733934 5.38656 2 1.0738901 0.31327367 0.918073 -0.733934 3 0.65119125 1.0738901 -0.105751 0.918073 4 0.70220182 1.0738901 -0.208309E-02 0.918073 5 0.70320786 0.70220182 0.627954E-05 -0.208309E-02 6 0.70320484 0.70320786 -0.268983E-08 0.627954E-05 Interval small enough for convergence. NEWTON Step X F(X) FP(X) 0 0.20000000E-03 -0.999800 -0.125000E+10 1 0.19999920E-03 0.119953E-04 -0.125003E+10 The stepsize is small enough for convergence. NEWTON Step X F(X) FP(X) 0 2.0000000 5.38656 7.39156 1 1.2712554 1.55914 3.57506 2 0.83513975 0.290802 2.33946 3 0.71083678 0.159089E-01 2.09135 4 0.70322980 0.518561E-04 2.07775 5 0.70320484 0.552829E-09 2.07771 The function norm is small enough for convergence. REGULA FALSI Step XA XB F(XA) F(XB) 0 0.20000000E-03 2.0000000 -0.999800 5.38656 1 0.31327367 2.0000000 -0.733934 5.38656 2 0.51553618 2.0000000 -0.363075 5.38656 3 0.60927634 2.0000000 -0.187830 5.38656 4 0.65613691 2.0000000 -0.958884E-01 5.38656 5 0.67964119 2.0000000 -0.484732E-01 5.38656 6 0.69141701 2.0000000 -0.243693E-01 5.38656 7 0.69731050 2.0000000 -0.122160E-01 5.38656 8 0.70025814 2.0000000 -0.611468E-02 5.38656 9 0.70173190 2.0000000 -0.305841E-02 5.38656 10 0.70246862 2.0000000 -0.152916E-02 5.38656 11 0.70283687 2.0000000 -0.764417E-03 5.38656 12 0.70302093 2.0000000 -0.382091E-03 5.38656 13 0.70311292 2.0000000 -0.190978E-03 5.38656 14 0.70315890 2.0000000 -0.954526E-04 5.38656 15 0.70318188 2.0000000 -0.477077E-04 5.38656 16 0.70319336 2.0000000 -0.238444E-04 5.38656 17 0.70319910 2.0000000 -0.119174E-04 5.38656 18 0.70320197 2.0000000 -0.595633E-05 5.38656 19 0.70320341 2.0000000 -0.297697E-05 5.38656 20 0.70320412 2.0000000 -0.148789E-05 5.38656 21 0.70320448 2.0000000 -0.743644E-06 5.38656 Function small enough for convergence. SECANT Step X F(X) -1 0.20000000E-03 -0.999800 0 2.0000000 5.38656 1 0.31327367 -0.733934 2 0.51553618 -0.363075 3 0.71355312 0.215964E-01 4 0.70243597 -0.159696E-02 5 0.70320144 -0.707529E-05 6 0.70320484 0.232331E-08 Function small enough for convergence. Problem number 7 F(X) = X**3, only linear Newton convergence. We seek roots between -1000.00 and 1000.00 Number of known roots = 1 Tabulated solutions: X F(X) 0.0000000 0.0000000 Number of starting points = 2 I XSTART(I), F(XSTART(I)) 1 1.0000000 1.0000000 2 -1000.0000 -0.10000000E+10 BISECTION Step XA XB F(XA) F(XB) 0 -1000.0000 1.0000000 -0.100000E+10 1.00000 1 -499.50000 1.0000000 -0.124625E+09 1.00000 2 -249.25000 1.0000000 -0.154848E+08 1.00000 3 -124.12500 1.0000000 -0.191240E+07 1.00000 4 -61.562500 1.0000000 -233318. 1.00000 5 -30.281250 1.0000000 -27766.5 1.00000 6 -14.640625 1.0000000 -3138.19 1.00000 7 -6.8203125 1.0000000 -317.258 1.00000 8 -2.9101563 1.0000000 -24.6461 1.00000 9 -0.95507813 1.0000000 -0.871198 1.00000 10 -0.95507813 0.22460938E-01 -0.871198 0.113314E-04 11 -0.46630859 0.22460938E-01 -0.101396 0.113314E-04 12 -0.22192383 0.22460938E-01 -0.109298E-01 0.113314E-04 13 -0.99731445E-01 0.22460938E-01 -0.991965E-03 0.113314E-04 14 -0.38635254E-01 0.22460938E-01 -0.576702E-04 0.113314E-04 15 -0.80871582E-02 0.22460938E-01 -0.528917E-06 0.113314E-04 Function small enough for convergence. BRENT Step XA XB F(XA) F(XB) 0 -1000.0000 1.0000000 -0.100000E+10 1.00000 1 0.99999750 -1000.0000 0.999993 -0.100000E+10 2 0.66666583 -1000.0000 0.296295 -0.100000E+10 3 -499.66667 0.66666583 -0.124750E+09 0.296295 4 0.66666400 -499.66667 0.296293 -0.124750E+09 5 0.44444328 -499.66667 0.877908E-01 -0.124750E+09 6 -249.61111 0.44444328 -0.155522E+08 0.877908E-01 7 0.44444187 -249.61111 0.877900E-01 -0.155522E+08 8 0.29629505 -249.61111 0.260120E-01 -0.155522E+08 9 -124.65741 0.29629505 -0.193711E+07 0.260120E-01 10 0.29629337 -124.65741 0.260115E-01 -0.193711E+07 11 0.19752947 -124.65741 0.770718E-02 -0.193711E+07 12 -62.229939 0.19752947 -240990. 0.770718E-02 13 0.19752748 -62.229939 0.770695E-02 -240990. 14 0.13168565 -62.229939 0.228358E-02 -240990. 15 -31.049127 0.13168565 -29932.9 0.228358E-02 16 0.13168327 -31.049127 0.228345E-02 -29932.9 17 0.87789646E-01 -31.049127 0.676597E-03 -29932.9 18 -15.480669 0.87789646E-01 -3709.96 0.676597E-03 19 0.87786807E-01 -15.480669 0.676531E-03 -3709.96 20 0.58525489E-01 -15.480669 0.200463E-03 -3709.96 21 -7.7110716 0.58525489E-01 -458.505 0.200463E-03 22 0.58522093E-01 -7.7110716 0.200429E-03 -458.505 23 0.39015869E-01 -7.7110716 0.593914E-04 -458.505 24 -3.8360279 0.39015869E-01 -56.4476 0.593914E-04 25 0.39011792E-01 -3.8360279 0.593728E-04 -56.4476 Maximum number of steps taken. NEWTON Step X F(X) FP(X) 0 1.0000000 1.00000 3.00000 1 0.66666667 0.296296 1.33333 2 0.44444444 0.877915E-01 0.592593 3 0.29629630 0.260123E-01 0.263374 4 0.19753086 0.770735E-02 0.117055 5 0.13168724 0.228366E-02 0.520246E-01 6 0.87791495E-01 0.676639E-03 0.231220E-01 7 0.58527663E-01 0.200486E-03 0.102765E-01 8 0.39018442E-01 0.594032E-04 0.456732E-02 9 0.26012295E-01 0.176009E-04 0.202992E-02 10 0.17341530E-01 0.521510E-05 0.902186E-03 11 0.11561020E-01 0.154521E-05 0.400972E-03 12 0.77073466E-02 0.457841E-06 0.178210E-03 The function norm is small enough for convergence. NEWTON Step X F(X) FP(X) 0 -1000.0000 -0.100000E+10 0.300000E+07 1 -666.66667 -0.296296E+09 0.133333E+07 2 -444.44444 -0.877915E+08 592593. 3 -296.29630 -0.260123E+08 263374. 4 -197.53086 -0.770735E+07 117055. 5 -131.68724 -0.228366E+07 52024.6 6 -87.791495 -676639. 23122.0 7 -58.527663 -200486. 10276.5 8 -39.018442 -59403.2 4567.32 9 -26.012295 -17600.9 2029.92 10 -17.341530 -5215.10 902.186 11 -11.561020 -1545.21 400.972 12 -7.7073466 -457.841 178.210 13 -5.1382311 -135.657 79.2043 14 -3.4254874 -40.1945 35.2019 15 -2.2836583 -11.9095 15.6453 16 -1.5224388 -3.52874 6.95346 17 -1.0149592 -1.04555 3.09043 18 -0.67663948 -0.309793 1.37352 19 -0.45109299 -0.917906E-01 0.610455 20 -0.30072866 -0.271972E-01 0.271313 21 -0.20048577 -0.805843E-02 0.120584 22 -0.13365718 -0.238768E-02 0.535927E-01 23 -0.89104788E-01 -0.707462E-03 0.238190E-01 24 -0.59403192E-01 -0.209618E-03 0.105862E-01 25 -0.39602128E-01 -0.621091E-04 0.470499E-02 Took maximum number of steps without convergence. REGULA FALSI Step XA XB F(XA) F(XB) 0 -1000.0000 1.0000000 -0.100000E+10 1.00000 1 -1000.0000 0.99999900 -0.100000E+10 0.999997 2 -1000.0000 0.99999800 -0.100000E+10 0.999994 3 -1000.0000 0.99999700 -0.100000E+10 0.999991 4 -1000.0000 0.99999600 -0.100000E+10 0.999988 5 -1000.0000 0.99999500 -0.100000E+10 0.999985 6 -1000.0000 0.99999399 -0.100000E+10 0.999982 7 -1000.0000 0.99999299 -0.100000E+10 0.999979 8 -1000.0000 0.99999199 -0.100000E+10 0.999976 9 -1000.0000 0.99999099 -0.100000E+10 0.999973 10 -1000.0000 0.99998999 -0.100000E+10 0.999970 11 -1000.0000 0.99998899 -0.100000E+10 0.999967 12 -1000.0000 0.99998799 -0.100000E+10 0.999964 13 -1000.0000 0.99998699 -0.100000E+10 0.999961 14 -1000.0000 0.99998599 -0.100000E+10 0.999958 15 -1000.0000 0.99998499 -0.100000E+10 0.999955 16 -1000.0000 0.99998398 -0.100000E+10 0.999952 17 -1000.0000 0.99998298 -0.100000E+10 0.999949 18 -1000.0000 0.99998198 -0.100000E+10 0.999946 19 -1000.0000 0.99998098 -0.100000E+10 0.999943 20 -1000.0000 0.99997998 -0.100000E+10 0.999940 21 -1000.0000 0.99997898 -0.100000E+10 0.999937 22 -1000.0000 0.99997798 -0.100000E+10 0.999934 23 -1000.0000 0.99997698 -0.100000E+10 0.999931 24 -1000.0000 0.99997598 -0.100000E+10 0.999928 25 -1000.0000 0.99997498 -0.100000E+10 0.999925 Took maximum number of steps without convergence. SECANT Step X F(X) -1 1.0000000 1.00000 0 -1000.0000 -0.100000E+10 1 0.99999900 0.999997 2 0.99999800 0.999994 3 0.66666567 0.296295 4 0.52631491 0.145793 5 0.39035529 0.594813E-01 6 0.29665958 0.261081E-01 7 0.22336070 0.111435E-01 8 0.16877841 0.480785E-02 9 0.12735809 0.206576E-02 10 0.96153997E-01 0.889001E-03 11 0.72580375E-01 0.382347E-03 12 0.54790504E-01 0.164481E-03 13 0.41359779E-01 0.707513E-04 14 0.31221675E-01 0.304347E-04 15 0.23568515E-01 0.130917E-04 16 0.17791355E-01 0.563154E-05 17 0.13430294E-01 0.242246E-05 18 0.10138229E-01 0.104204E-05 19 0.76531228E-02 0.448246E-06 Function small enough for convergence. Problem number 8 F(X) = COS(X) - X We seek roots between -10.0000 and 10.0000 Number of known roots = 1 Tabulated solutions: X F(X) 0.73908513 0.0000000 Number of starting points = 2 I XSTART(I), F(XSTART(I)) 1 1.0000000 -0.45969769 2 0.50000000 0.37758256 BISECTION Step XA XB F(XA) F(XB) 0 1.0000000 0.50000000 -0.459698 0.377583 1 0.75000000 0.50000000 -0.183111E-01 0.377583 2 0.75000000 0.62500000 -0.183111E-01 0.185963 3 0.75000000 0.68750000 -0.183111E-01 0.853349E-01 4 0.75000000 0.71875000 -0.183111E-01 0.338794E-01 5 0.75000000 0.73437500 -0.183111E-01 0.787473E-02 6 0.74218750 0.73437500 -0.519571E-02 0.787473E-02 7 0.74218750 0.73828125 -0.519571E-02 0.134515E-02 8 0.74023438 0.73828125 -0.192387E-02 0.134515E-02 9 0.73925781 0.73828125 -0.289009E-03 0.134515E-02 10 0.73925781 0.73876953 -0.289009E-03 0.528158E-03 11 0.73925781 0.73901367 -0.289009E-03 0.119597E-03 12 0.73913574 0.73901367 -0.847007E-04 0.119597E-03 13 0.73913574 0.73907471 -0.847007E-04 0.174493E-04 14 0.73910522 0.73907471 -0.336253E-04 0.174493E-04 15 0.73908997 0.73907471 -0.808791E-05 0.174493E-04 16 0.73908997 0.73908234 -0.808791E-05 0.468074E-05 17 0.73908615 0.73908234 -0.170358E-05 0.468074E-05 18 0.73908615 0.73908424 -0.170358E-05 0.148858E-05 19 0.73908520 0.73908424 -0.107502E-06 0.148858E-05 Interval small enough for convergence. BRENT Step XA XB F(XA) F(XB) 0 0.50000000 1.0000000 0.377583 -0.459698 1 0.72548159 1.0000000 0.226984E-01 -0.459698 2 0.73922479 0.72548159 -0.233744E-03 0.226984E-01 3 0.73908471 0.73922479 0.707057E-06 -0.233744E-03 Function small enough for convergence. NEWTON Step X F(X) FP(X) 0 1.0000000 -0.459698 -1.84147 1 0.75036387 -0.189231E-01 -1.68190 2 0.73911289 -0.464559E-04 -1.67363 3 0.73908513 -0.284721E-09 -1.67361 The function norm is small enough for convergence. NEWTON Step X F(X) FP(X) 0 0.50000000 0.377583 -1.47943 1 0.75522242 -0.271033E-01 -1.68545 2 0.73914167 -0.946154E-04 -1.67365 3 0.73908513 -0.118098E-08 -1.67361 The function norm is small enough for convergence. REGULA FALSI Step XA XB F(XA) F(XB) 0 1.0000000 0.50000000 -0.459698 0.377583 1 1.0000000 0.72548159 -0.459698 0.226984E-01 2 1.0000000 0.73839862 -0.459698 0.114878E-02 3 1.0000000 0.73905073 -0.459698 0.575753E-04 4 1.0000000 0.73908341 -0.459698 0.288417E-05 5 1.0000000 0.73908505 -0.459698 0.144476E-06 Function small enough for convergence. SECANT Step X F(X) -1 1.0000000 -0.459698 0 0.50000000 0.377583 1 0.72548159 0.226984E-01 2 0.73990339 -0.136969E-02 3 0.73908266 0.414110E-05 4 0.73908513 0.747874E-09 Function small enough for convergence. Problem number 9 The Newton Baffler We seek roots between -4.00000 and 16.0000 Number of known roots = 1 Tabulated solutions: X F(X) 6.2500000 0.0000000 Number of starting points = 3 I XSTART(I), F(XSTART(I)) 1 11.250000 4.0625000 2 5.2500000 -1.0625000 3 6.3500000 0.20000000 BISECTION Step XA XB F(XA) F(XB) 0 5.2500000 11.250000 -1.06250 4.06250 1 5.2500000 8.2500000 -1.06250 1.81250 2 5.2500000 6.7500000 -1.06250 0.687500 3 6.0000000 6.7500000 -0.500000 0.687500 4 6.0000000 6.3750000 -0.500000 0.250000 5 6.1875000 6.3750000 -0.125000 0.250000 6 6.1875000 6.2812500 -0.125000 0.625000E-01 7 6.2343750 6.2812500 -0.312500E-01 0.625000E-01 8 6.2343750 6.2578125 -0.312500E-01 0.156250E-01 9 6.2460938 6.2578125 -0.781250E-02 0.156250E-01 10 6.2460938 6.2519531 -0.781250E-02 0.390625E-02 11 6.2490234 6.2519531 -0.195313E-02 0.390625E-02 12 6.2490234 6.2504883 -0.195313E-02 0.976563E-03 13 6.2497559 6.2504883 -0.488281E-03 0.976563E-03 14 6.2497559 6.2501221 -0.488281E-03 0.244141E-03 15 6.2499390 6.2501221 -0.122070E-03 0.244141E-03 16 6.2499390 6.2500305 -0.122070E-03 0.610352E-04 17 6.2499847 6.2500305 -0.305176E-04 0.610352E-04 18 6.2499847 6.2500076 -0.305176E-04 0.152588E-04 19 6.2499962 6.2500076 -0.762939E-05 0.152588E-04 20 6.2499962 6.2500019 -0.762939E-05 0.381470E-05 21 6.2499990 6.2500019 -0.190735E-05 0.381470E-05 22 6.2499990 6.2500005 -0.190735E-05 0.953674E-06 Function small enough for convergence. BRENT Step XA XB F(XA) F(XB) 0 5.2500000 11.250000 -1.06250 4.06250 1 6.4939024 5.2500000 0.487805 -1.06250 2 6.1025074 6.4939024 -0.294985 0.487805 3 6.2500000 6.4939024 0.00000 0.487805 Function small enough for convergence. MULLER Step XA XB XC F(XA) F(XB) F(XC) 0 11.2500 5.25000 6.35000 4.06250 -1.06250 0.200000 1 5.25000 6.35000 6.16698 -1.06250 0.200000 -0.166035 2 6.35000 6.16698 6.25388 0.200000 -0.166035 0.776319E-02 3 6.16698 6.25388 6.25000 -0.166035 0.776319E-02 0.00000 Function small enough for convergence. NEWTON Step X F(X) FP(X) 0 11.250000 4.06250 0.750000 1 5.8333333 -0.625000 0.750000 2 6.6666667 0.625000 0.750000 3 5.8333333 -0.625000 0.750000 4 6.6666667 0.625000 0.750000 5 5.8333333 -0.625000 0.750000 6 6.6666667 0.625000 0.750000 7 5.8333333 -0.625000 0.750000 8 6.6666667 0.625000 0.750000 9 5.8333333 -0.625000 0.750000 10 6.6666667 0.625000 0.750000 11 5.8333333 -0.625000 0.750000 12 6.6666667 0.625000 0.750000 13 5.8333333 -0.625000 0.750000 14 6.6666667 0.625000 0.750000 15 5.8333333 -0.625000 0.750000 16 6.6666667 0.625000 0.750000 17 5.8333333 -0.625000 0.750000 18 6.6666667 0.625000 0.750000 19 5.8333333 -0.625000 0.750000 20 6.6666667 0.625000 0.750000 21 5.8333333 -0.625000 0.750000 22 6.6666667 0.625000 0.750000 23 5.8333333 -0.625000 0.750000 24 6.6666667 0.625000 0.750000 25 5.8333333 -0.625000 0.750000 Took maximum number of steps without convergence. NEWTON Step X F(X) FP(X) 0 5.2500000 -1.06250 0.750000 1 6.6666667 0.625000 0.750000 2 5.8333333 -0.625000 0.750000 3 6.6666667 0.625000 0.750000 4 5.8333333 -0.625000 0.750000 5 6.6666667 0.625000 0.750000 6 5.8333333 -0.625000 0.750000 7 6.6666667 0.625000 0.750000 8 5.8333333 -0.625000 0.750000 9 6.6666667 0.625000 0.750000 10 5.8333333 -0.625000 0.750000 11 6.6666667 0.625000 0.750000 12 5.8333333 -0.625000 0.750000 13 6.6666667 0.625000 0.750000 14 5.8333333 -0.625000 0.750000 15 6.6666667 0.625000 0.750000 16 5.8333333 -0.625000 0.750000 17 6.6666667 0.625000 0.750000 18 5.8333333 -0.625000 0.750000 19 6.6666667 0.625000 0.750000 20 5.8333333 -0.625000 0.750000 21 6.6666667 0.625000 0.750000 22 5.8333333 -0.625000 0.750000 23 6.6666667 0.625000 0.750000 24 5.8333333 -0.625000 0.750000 25 6.6666667 0.625000 0.750000 Took maximum number of steps without convergence. NEWTON Step X F(X) FP(X) 0 6.3500000 0.200000 2.00000 1 6.2500000 0.00000 2.00000 The function norm is small enough for convergence. REGULA FALSI Step XA XB F(XA) F(XB) 0 5.2500000 11.250000 -1.06250 4.06250 1 5.2500000 6.4939024 -1.06250 0.487805 2 6.1025074 6.4939024 -0.294985 0.487805 3 6.1025074 6.2500000 -0.294985 0.00000 Function small enough for convergence. SECANT Step X F(X) -1 11.250000 4.06250 0 5.2500000 -1.06250 1 6.4939024 0.487805 2 6.1025074 -0.294985 3 6.2500000 0.00000 Function small enough for convergence. SECANT Step X F(X) -1 5.2500000 -1.06250 0 6.3500000 0.200000 1 6.1757426 -0.148515 2 6.2500000 0.00000 Function small enough for convergence. Problem number 10 The Repeller We seek roots between -10.0000 and 10.0000 Number of known roots = 1 Tabulated solutions: X F(X) 0.0000000 0.0000000 Number of starting points = 3 I XSTART(I), F(XSTART(I)) 1 1.0000000 0.19801980 2 -0.14000000 -0.94594595 3 0.41000000E-01 0.70199469 BISECTION Step XA XB F(XA) F(XB) 0 -0.14000000 1.0000000 -0.945946 0.198020 1 -0.14000000 0.43000000 -0.945946 0.441252 2 -0.14000000 0.14500000 -0.945946 0.934730 3 -0.14000000 0.25000000E-02 -0.945946 0.499688E-01 4 -0.68750000E-01 0.25000000E-02 -0.933687 0.499688E-01 5 -0.33125000E-01 0.25000000E-02 -0.596994 0.499688E-01 6 -0.15312500E-01 0.25000000E-02 -0.299234 0.499688E-01 7 -0.64062500E-02 0.25000000E-02 -0.127601 0.499688E-01 8 -0.19531250E-02 0.25000000E-02 -0.390476E-01 0.499688E-01 9 -0.19531250E-02 0.27343750E-03 -0.390476E-01 0.546871E-02 10 -0.83984375E-03 0.27343750E-03 -0.167957E-01 0.546871E-02 11 -0.28320313E-03 0.27343750E-03 -0.566402E-02 0.546871E-02 12 -0.48828125E-05 0.27343750E-03 -0.976562E-04 0.546871E-02 13 -0.48828125E-05 0.13427734E-03 -0.976562E-04 0.268554E-02 14 -0.48828125E-05 0.64697266E-04 -0.976562E-04 0.129394E-02 15 -0.48828125E-05 0.29907227E-04 -0.976562E-04 0.598144E-03 16 -0.48828125E-05 0.12512207E-04 -0.976562E-04 0.250244E-03 17 -0.48828125E-05 0.38146973E-05 -0.976562E-04 0.762939E-04 18 -0.53405762E-06 0.38146973E-05 -0.106812E-04 0.762939E-04 19 -0.53405762E-06 0.16403198E-05 -0.106812E-04 0.328064E-04 20 -0.53405762E-06 0.55313110E-06 -0.106812E-04 0.110626E-04 21 -0.53405762E-06 0.95367432E-08 -0.106812E-04 0.190735E-06 Interval small enough for convergence. BRENT Step XA XB F(XA) F(XB) 0 -0.14000000 1.0000000 -0.945946 0.198020 1 0.80266667 -0.14000000 0.245361 -0.945946 2 0.33133333 -0.14000000 0.553228 -0.945946 3 0.95666667E-01 -0.14000000 0.999020 -0.945946 4 -0.25382065E-01 0.95666667E-01 -0.476916 0.999020 5 0.53504043E-01 -0.25382065E-01 0.831927 -0.476916 6 0.33624506E-02 -0.25382065E-01 0.671731E-01 -0.476916 7 -0.18633815E-03 0.33624506E-02 -0.372675E-02 0.671731E-01 8 0.19898775E-06 -0.18633815E-03 0.397975E-05 -0.372675E-02 9 -0.30101265E-06 0.19898775E-06 -0.602025E-05 0.397975E-05 Interval small enough for convergence. MULLER Step XA XB XC F(XA) F(XB) F(XC) 0 1.00000 -0.140000 0.410000E-01 0.198020 -0.945946 0.701995 1 -0.140000 0.410000E-01 -0.436705E-01 -0.945946 0.701995 -0.733520 2 0.410000E-01 -0.436705E-01 0.780687E-02 0.701995 -0.733520 0.155192 3 -0.436705E-01 0.780687E-02 -0.139278E-02 -0.733520 0.155192 -0.278503E-01 4 0.780687E-02 -0.139278E-02 0.418288E-04 0.155192 -0.278503E-01 0.836576E-03 5 -0.139278E-02 0.418288E-04 -0.452930E-07 -0.278503E-01 0.836576E-03 -0.905861E-06 Function small enough for convergence. NEWTON Step X F(X) FP(X) 0 1.0000000 0.198020 -0.970493E-02 1 21.404040 0.934383E-02 -0.218263E-04 The iterate X = 21.4040 has left the region [XMIN,XMAX]. NEWTON Step X F(X) FP(X) 0 -0.14000000 -0.945946 -0.109569 1 -8.7733333 -0.227934E-01 -0.129868E-03 2 -184.28560 -0.108527E-02 -0.294454E-06 The iterate X = -184.286 has left the region [XMIN,XMAX]. NEWTON Step X F(X) FP(X) 0 0.41000000E-01 0.701995 0.609693 1 -1.1103908 -0.178668 -0.791581E-02 2 -23.681386 -0.844530E-02 -0.178305E-04 The iterate X = -23.6814 has left the region [XMIN,XMAX]. REGULA FALSI Step XA XB F(XA) F(XB) 0 -0.14000000 1.0000000 -0.945946 0.198020 1 -0.14000000 0.80266667 -0.945946 0.245361 2 -0.14000000 0.60851544 -0.945946 0.320026 3 -0.14000000 0.41929758 -0.945946 0.451318 4 -0.14000000 0.23864389 -0.945946 0.712892 5 -0.14000000 0.75920195E-01 -0.945946 0.963217 6 -0.33016573E-01 0.75920195E-01 -0.595425 0.963217 7 -0.33016573E-01 0.85989049E-02 -0.595425 0.170716 8 -0.67409516E-03 0.85989049E-02 -0.134813E-01 0.170716 9 -0.67409516E-03 0.45909392E-05 -0.134813E-01 0.918188E-04 10 -0.20719341E-09 0.45909392E-05 -0.414387E-08 0.918188E-04 Function small enough for convergence. SECANT Step X F(X) -1 1.0000000 0.198020 0 -0.14000000 -0.945946 1 0.80266667 0.245361 2 0.60851544 0.320026 3 1.4406779 0.138158 4 2.0728376 0.962621E-01 5 3.5253206 0.566868E-01 6 5.6058296 0.356658E-01 7 9.1357730 0.218893E-01 8 14.744482 0.135638E-01 Iterate has left the region [XMIN,XMAX]. SECANT Step X F(X) -1 -0.14000000 -0.945946 0 0.41000000E-01 0.701995 1 -0.36102922E-01 -0.638796 2 0.63141223E-03 0.126277E-01 3 -0.80676332E-04 -0.161353E-02 4 0.28054356E-08 0.561087E-07 Function small enough for convergence. Problem number 11 The Pinhead We seek roots between 0.00000 and 10.0000 Number of known roots = 2 Tabulated solutions: X F(X) -2.0000000 0.0000000 2.0000000 0.0000000 Number of starting points = 3 I XSTART(I), F(XSTART(I)) 1 0.25000000 255.89656 2 5.0000000 -0.60900000E-01 3 1.1000000 0.62051319 BISECTION Step XA XB F(XA) F(XB) 0 5.0000000 0.25000000 -0.609000E-01 255.897 1 2.6250000 0.25000000 -0.414388E-01 255.897 2 2.6250000 1.4375000 -0.414388E-01 0.171690 3 2.0312500 1.4375000 -0.375830E-02 0.171690 4 2.0312500 1.7343750 -0.375830E-02 0.480167E-01 5 2.0312500 1.8828125 -0.375830E-02 0.170741E-01 6 2.0312500 1.9570313 -0.375830E-02 0.567246E-02 7 2.0312500 1.9941406 -0.375830E-02 0.737818E-03 8 2.0126953 1.9941406 -0.156205E-02 0.737818E-03 9 2.0034180 1.9941406 -0.425427E-03 0.737818E-03 10 2.0034180 1.9987793 -0.425427E-03 0.152821E-03 11 2.0010986 1.9987793 -0.137141E-03 0.152821E-03 12 2.0010986 1.9999390 -0.137141E-03 0.762998E-05 13 2.0005188 1.9999390 -0.648078E-04 0.762998E-05 14 2.0002289 1.9999390 -0.286020E-04 0.762998E-05 15 2.0000839 1.9999390 -0.104893E-04 0.762998E-05 16 2.0000114 1.9999390 -0.143049E-05 0.762998E-05 17 2.0000114 1.9999752 -0.143049E-05 0.309954E-05 18 2.0000114 1.9999933 -0.143049E-05 0.834472E-06 Function small enough for convergence. BRENT Step XA XB F(XA) F(XB) 0 5.0000000 0.25000000 -0.609000E-01 255.897 1 4.9988698 0.25000000 -0.608986E-01 255.897 2 2.6244349 0.25000000 -0.414207E-01 255.897 3 1.4372175 2.6244349 0.171874 -0.414207E-01 4 2.3938841 1.4372175 -0.320500E-01 0.171874 5 1.9155508 2.3938841 0.117720E-01 -0.320500E-01 6 2.0440468 1.9155508 -0.521557E-02 0.117720E-01 7 2.0045957 1.9155508 -0.571181E-03 0.117720E-01 8 1.9999684 2.0045957 0.394708E-05 -0.571181E-03 9 2.0000002 1.9999684 -0.226996E-07 0.394708E-05 Function small enough for convergence. MULLER Step XA XB XC F(XA) F(XB) F(XC) 0 0.250000 5.00000 1.10000 255.897 -0.609000E-01 0.620513 1 0.250000 1.10000 1.10252 255.897 0.620513 0.614295 2 1.10000 1.10252 1.87528 0.620513 0.614295 0.183607E-01 3 1.10252 1.87528 1.85431 0.614295 0.183607E-01 0.220803E-01 4 1.87528 1.85431 2.08198 0.183607E-01 0.220803E-01 -0.927787E-02 5 1.87528 2.08198 1.99779 0.183607E-01 -0.927787E-02 0.277207E-03 6 2.08198 1.99779 1.99997 -0.927787E-02 0.277207E-03 0.365588E-05 7 1.99779 1.99997 2.00000 0.277207E-03 0.365588E-05 0.774109E-09 Function small enough for convergence. NEWTON Step X F(X) FP(X) 0 0.25000000 255.897 -4094.69 1 0.31249474 104.795 -1342.11 2 0.39057697 42.9071 -440.052 3 0.48808181 17.5583 -144.407 4 0.60967080 7.17546 -47.4875 5 0.76077305 2.92274 -15.6958 6 0.94698471 1.18095 -5.25224 7 1.1718314 0.467822 -1.81023 8 1.4302634 0.176466 -0.668313 9 1.6943102 0.588468E-01 -0.286481 10 1.8997230 0.142784E-01 -0.161662 11 1.9880452 0.151695E-02 -0.128804 12 1.9998224 0.222026E-04 -0.125056 13 2.0000000 0.492694E-08 -0.125000 The function norm is small enough for convergence. NEWTON Step X F(X) FP(X) 0 5.0000000 -0.609000E-01 -0.128000E-02 1 -42.578123 -0.624997E-01 0.285843E-07 The iterate X = -42.5781 has left the region [XMIN,XMAX]. NEWTON Step X F(X) FP(X) 0 1.1000000 0.620513 -2.48368 1 1.3498359 0.238715 -0.892596 2 1.6172744 0.836723E-01 -0.361527 3 1.8487155 0.231090E-01 -0.185229 4 1.9734747 0.342859E-02 -0.133629 5 1.9991321 0.108606E-03 -0.125272 6 1.9999991 0.117645E-06 -0.125000 The function norm is small enough for convergence. REGULA FALSI Step XA XB F(XA) F(XB) 0 5.0000000 0.25000000 -0.609000E-01 255.897 1 4.9988698 0.25000000 -0.608986E-01 255.897 2 4.9977400 0.25000000 -0.608971E-01 255.897 3 4.9966104 0.25000000 -0.608957E-01 255.897 4 4.9954811 0.25000000 -0.608942E-01 255.897 5 4.9943521 0.25000000 -0.608928E-01 255.897 6 4.9932234 0.25000000 -0.608913E-01 255.897 7 4.9920950 0.25000000 -0.608898E-01 255.897 8 4.9909669 0.25000000 -0.608884E-01 255.897 9 4.9898391 0.25000000 -0.608869E-01 255.897 10 4.9887116 0.25000000 -0.608855E-01 255.897 11 4.9875844 0.25000000 -0.608840E-01 255.897 12 4.9864575 0.25000000 -0.608825E-01 255.897 13 4.9853309 0.25000000 -0.608811E-01 255.897 14 4.9842045 0.25000000 -0.608796E-01 255.897 15 4.9830785 0.25000000 -0.608782E-01 255.897 16 4.9819528 0.25000000 -0.608767E-01 255.897 17 4.9808273 0.25000000 -0.608752E-01 255.897 18 4.9797022 0.25000000 -0.608738E-01 255.897 19 4.9785773 0.25000000 -0.608723E-01 255.897 20 4.9774528 0.25000000 -0.608708E-01 255.897 21 4.9763285 0.25000000 -0.608693E-01 255.897 22 4.9752045 0.25000000 -0.608679E-01 255.897 23 4.9740808 0.25000000 -0.608664E-01 255.897 24 4.9729575 0.25000000 -0.608649E-01 255.897 25 4.9718344 0.25000000 -0.608634E-01 255.897 Took maximum number of steps without convergence. SECANT Step X F(X) -1 0.25000000 255.897 0 5.0000000 -0.609000E-01 1 4.9988698 -0.608986E-01 2 -42.551241 -0.624997E-01 Iterate has left the region [XMIN,XMAX]. SECANT Step X F(X) -1 5.0000000 -0.609000E-01 0 1.1000000 0.620513 1 4.6514450 -0.603638E-01 2 4.3365884 -0.596725E-01 3 -22.841675 -0.624963E-01 Iterate has left the region [XMIN,XMAX]. Problem number 12 Flat Stanley (ALL derivatives are zero at the root.) We seek roots between -4.00000 and 4.00000 Number of known roots = 1 Tabulated solutions: X F(X) 1.0000000 0.0000000 Number of starting points = 3 I XSTART(I), F(XSTART(I)) 1 2.0000000 367.87944 2 0.50000000 -9.1578194 3 4.0000000 2684.5180 BISECTION Step XA XB F(XA) F(XB) 0 0.50000000 2.0000000 -9.15782 367.879 1 0.50000000 1.2500000 -9.15782 0.281338E-04 2 0.87500000 1.2500000 -0.200476E-25 0.281338E-04 Function small enough for convergence. BRENT Step XA XB F(XA) F(XB) 0 0.50000000 2.0000000 -9.15782 367.879 1 0.53643335 2.0000000 -4.41715 367.879 2 0.56997755 2.0000000 -1.92721 367.879 3 1.2849888 0.56997755 0.128115E-02 -1.92721 4 1.2845138 0.56997755 0.122745E-02 -1.92721 5 1.2736620 0.56997755 0.434696E-03 -1.92721 6 0.92181978 1.2736620 -0.689877E-69 0.434696E-03 Function small enough for convergence. MULLER Step XA XB XC F(XA) F(XB) F(XC) 0 2.00000 0.500000 4.00000 367.879 -9.15782 2684.52 1 0.500000 2.00000 1.08991 -9.15782 367.879 0.168319E-51 Function small enough for convergence. NEWTON Step X F(X) FP(X) 0 2.0000000 367.879 1103.64 1 1.6666667 70.2661 579.696 2 1.5454545 18.9255 267.936 3 1.4748201 5.62626 116.964 4 1.4267175 1.75816 49.3752 5 1.3911094 0.566437 20.3842 6 1.3633214 0.186312 8.28241 7 1.3408264 0.622096E-01 3.32512 8 1.3221174 0.210103E-01 1.32247 9 1.3062302 0.715988E-02 0.522026 10 1.2925147 0.245770E-02 0.204790 11 1.2805136 0.848693E-03 0.799242E-01 12 1.2698949 0.294546E-03 0.310553E-01 13 1.2604103 0.102663E-03 0.120213E-01 14 1.2518702 0.359149E-04 0.463806E-02 15 1.2441267 0.126047E-04 0.178430E-02 16 1.2370625 0.443623E-05 0.684684E-03 17 1.2305833 0.156525E-05 0.262134E-03 18 1.2246121 0.553504E-06 0.100155E-03 The function norm is small enough for convergence. NEWTON Step X F(X) FP(X) 0 0.50000000 -9.15782 164.841 1 0.55555556 -2.81321 70.4181 2 0.59550562 -0.896511 29.3088 3 0.62609406 -0.292649 11.9794 4 0.65052346 -0.971692E-01 4.83111 5 0.67063666 -0.326761E-01 1.92830 6 0.68758224 -0.110973E-01 0.763370 7 0.70211953 -0.379868E-02 0.300186 8 0.71477398 -0.130874E-02 0.117390 9 0.72592261 -0.453324E-03 0.456911E-01 10 0.73584409 -0.157741E-03 0.177128E-01 11 0.74474957 -0.551037E-04 0.684280E-02 12 0.75280238 -0.193148E-04 0.263547E-02 13 0.76013117 -0.679033E-05 0.101232E-02 14 0.76683887 -0.239349E-05 0.387919E-03 15 0.77300895 -0.845643E-06 0.148333E-03 The function norm is small enough for convergence. NEWTON Step X F(X) FP(X) 0 4.0000000 2684.52 1093.69 1 1.5454545 18.9255 267.936 2 1.4748201 5.62626 116.964 3 1.4267175 1.75816 49.3752 4 1.3911094 0.566437 20.3842 5 1.3633214 0.186312 8.28241 6 1.3408264 0.622096E-01 3.32512 7 1.3221174 0.210103E-01 1.32247 8 1.3062302 0.715988E-02 0.522026 9 1.2925147 0.245770E-02 0.204790 10 1.2805136 0.848693E-03 0.799242E-01 11 1.2698949 0.294546E-03 0.310553E-01 12 1.2604103 0.102663E-03 0.120213E-01 13 1.2518702 0.359149E-04 0.463806E-02 14 1.2441267 0.126047E-04 0.178430E-02 15 1.2370625 0.443623E-05 0.684684E-03 16 1.2305833 0.156525E-05 0.262134E-03 17 1.2246121 0.553504E-06 0.100155E-03 The function norm is small enough for convergence. REGULA FALSI Step XA XB F(XA) F(XB) 0 0.50000000 2.0000000 -9.15782 367.879 1 0.53643335 2.0000000 -4.41715 367.879 2 0.55379797 2.0000000 -2.93902 367.879 3 0.56526022 2.0000000 -2.18957 367.879 4 0.57374908 2.0000000 -1.73524 367.879 5 0.58044492 2.0000000 -1.43080 367.879 6 0.58594462 2.0000000 -1.21303 367.879 7 0.59059192 2.0000000 -1.04986 367.879 8 0.59460267 2.0000000 -0.923283 367.879 9 0.59812103 2.0000000 -0.822388 367.879 10 0.60124792 2.0000000 -0.740196 367.879 11 0.60405664 2.0000000 -0.672029 367.879 12 0.60660205 2.0000000 -0.614642 367.879 13 0.60892622 2.0000000 -0.565712 367.879 14 0.61106207 2.0000000 -0.523532 367.879 15 0.61303587 2.0000000 -0.486823 367.879 16 0.61486885 2.0000000 -0.454607 367.879 17 0.61657841 2.0000000 -0.426124 367.879 18 0.61817901 2.0000000 -0.400774 367.879 19 0.61968275 2.0000000 -0.378079 367.879 20 0.62109988 2.0000000 -0.357651 367.879 21 0.62243913 2.0000000 -0.339174 367.879 22 0.62370803 2.0000000 -0.322388 367.879 23 0.62491308 2.0000000 -0.307077 367.879 24 0.62605994 2.0000000 -0.293058 367.879 25 0.62715357 2.0000000 -0.280178 367.879 Took maximum number of steps without convergence. SECANT Step X F(X) -1 2.0000000 367.879 0 0.50000000 -9.15782 1 0.53643335 -4.41715 2 0.57038031 -1.90597 3 0.59614592 -0.877898 4 0.61814781 -0.401256 5 0.63666989 -0.186385 6 0.65273639 -0.869573E-01 7 0.66678782 -0.408533E-01 8 0.67923901 -0.192808E-01 9 0.69036743 -0.913948E-02 10 0.70039651 -0.434782E-02 11 0.70949663 -0.207495E-02 12 0.71780429 -0.992997E-03 13 0.72542893 -0.476389E-03 14 0.73245997 -0.229050E-03 15 0.73897114 -0.110347E-03 16 0.74502390 -0.532552E-04 17 0.75066997 -0.257436E-04 18 0.75595319 -0.124629E-04 19 0.76091105 -0.604163E-05 20 0.76557581 -0.293245E-05 21 0.76997541 -0.142496E-05 22 0.77413418 -0.693167E-06 Function small enough for convergence. SECANT Step X F(X) -1 0.50000000 -9.15782 0 4.0000000 2684.52 1 0.51189912 -7.33838 2 0.52140817 -6.07992 3 0.56734884 -2.07027 4 0.59106908 -1.03413 5 0.61474324 -0.456758 6 0.63347184 -0.214475 7 0.65005078 -0.994752E-01 8 0.66439167 -0.467729E-01 9 0.67711909 -0.220410E-01 10 0.68846174 -0.104433E-01 11 0.69867530 -0.496450E-02 12 0.70793017 -0.236807E-02 13 0.71637108 -0.113272E-02 14 0.72411077 -0.543197E-03 15 0.73124222 -0.261073E-03 16 0.73784155 -0.125731E-03 17 0.74397228 -0.606616E-04 18 0.74968768 -0.293157E-04 19 0.75503289 -0.141885E-04 20 0.76004646 -0.687658E-05 21 0.76476149 -0.333699E-05 22 0.76920665 -0.162122E-05 23 0.77340686 -0.788491E-06 Function small enough for convergence. Problem number 13 Lazy Boy (Linear function, almost flat.) We seek roots between -0.100000E+14 and 0.100000E+14 Number of known roots = 1 Tabulated solutions: X F(X) 100.00000 0.0000000 Number of starting points = 3 I XSTART(I), F(XSTART(I)) 1 0.10000000E+09 0.99999900E-03 2 0.10000001E+09 0.99999913E-03 3 -0.10000000E+12 -1.0000000 BISECTION Step XA XB F(XA) F(XB) 0 -0.10000000E+12 0.10000000E+09 -1.00000 0.999999E-03 1 -0.49950000E+11 0.10000000E+09 -0.499500 0.999999E-03 2 -0.24925000E+11 0.10000000E+09 -0.249250 0.999999E-03 3 -0.12412500E+11 0.10000000E+09 -0.124125 0.999999E-03 4 -0.61562500E+10 0.10000000E+09 -0.615625E-01 0.999999E-03 5 -0.30281250E+10 0.10000000E+09 -0.302813E-01 0.999999E-03 6 -0.14640625E+10 0.10000000E+09 -0.146406E-01 0.999999E-03 7 -0.68203125E+09 0.10000000E+09 -0.682031E-02 0.999999E-03 8 -0.29101563E+09 0.10000000E+09 -0.291016E-02 0.999999E-03 9 -95507813. 0.10000000E+09 -0.955079E-03 0.999999E-03 10 -95507813. 2246093.8 -0.955079E-03 0.224599E-04 11 -46630859. 2246093.8 -0.466310E-03 0.224599E-04 12 -22192383. 2246093.8 -0.221925E-03 0.224599E-04 13 -9973144.5 2246093.8 -0.997324E-04 0.224599E-04 14 -3863525.4 2246093.8 -0.386363E-04 0.224599E-04 15 -808715.82 2246093.8 -0.808816E-05 0.224599E-04 16 -808715.82 718688.96 -0.808816E-05 0.718589E-05 17 -45013.428 718688.96 -0.451134E-06 0.718589E-05 Function small enough for convergence. BRENT Step XA XB F(XA) F(XB) 0 -0.10000000E+12 0.10000000E+09 -1.00000 0.999999E-03 1 100.00000 -0.10000000E+12 0.00000 -1.00000 Function small enough for convergence. MULLER Step XA XB XC F(XA) F(XB) F(XC) 0 0.100000E+09 0.100000E+09 -0.100000E+12 0.999999E-03 0.999999E-03 -1.00000 1 0.100000E+09 0.100000E+09 113160. 0.999999E-03 0.999999E-03 0.113060E-05 2 0.100000E+09 113160. 100.000 0.999999E-03 0.113060E-05 -0.251132E-15 Function small enough for convergence. NEWTON Step X F(X) FP(X) 0 0.10000000E+09 0.999999E-03 0.100000E-10 1 100.00000 0.00000 0.100000E-10 The function norm is small enough for convergence. NEWTON Step X F(X) FP(X) 0 0.10000001E+09 0.999999E-03 0.100000E-10 1 100.00000 -0.149012E-18 0.100000E-10 The function norm is small enough for convergence. NEWTON Step X F(X) FP(X) 0 -0.10000000E+12 -1.00000 0.100000E-10 1 99.999985 -0.152588E-15 0.100000E-10 The function norm is small enough for convergence. REGULA FALSI Step XA XB F(XA) F(XB) 0 -0.10000000E+12 0.10000000E+09 -1.00000 0.999999E-03 1 100.00000 0.10000000E+09 -0.595450E-19 0.999999E-03 Function small enough for convergence. SECANT Step X F(X) -1 0.10000000E+09 0.999999E-03 0 0.10000001E+09 0.999999E-03 1 100.07240 0.724015E-12 Function small enough for convergence. SECANT Step X F(X) -1 0.10000001E+09 0.999999E-03 0 -0.10000000E+12 -1.00000 1 100.00000 -0.189415E-18 Function small enough for convergence. Problem number 14 The Camel (double hump and some shallow roots.) We seek roots between -10.0000 and 10.0000 Number of known roots = 3 Tabulated solutions: X F(X) -0.15348049 0.88817842E-15 1.8190324 -0.88817842E-15 2.1274329 -0.88817842E-15 Number of starting points = 4 I XSTART(I), F(XSTART(I)) 1 3.0000000 1.1617054 2 -0.50000000 -4.1615385 3 0.0000000 5.9764706 4 2.1274200 -0.83786519E-05 BISECTION Step XA XB F(XA) F(XB) 0 -0.50000000 3.0000000 -4.16154 1.16171 1 -0.50000000 1.2500000 -4.16154 4.54974 2 -0.50000000 0.37500000 -4.16154 62.7183 3 -0.50000000 -0.62500000E-01 -4.16154 2.78158 4 -0.28125000 -0.62500000E-01 -2.19102 2.78158 5 -0.17187500 -0.62500000E-01 -0.404641 2.78158 6 -0.17187500 -0.11718750 -0.404641 0.929585 7 -0.17187500 -0.14453125 -0.404641 0.211845 8 -0.15820313 -0.14453125 -0.107698 0.211845 9 -0.15820313 -0.15136719 -0.107698 0.490929E-01 10 -0.15478516 -0.15136719 -0.300276E-01 0.490929E-01 11 -0.15478516 -0.15307617 -0.300276E-01 0.934895E-02 12 -0.15393066 -0.15307617 -0.103849E-01 0.934895E-02 13 -0.15350342 -0.15307617 -0.529426E-03 0.934895E-02 14 -0.15350342 -0.15328979 -0.529426E-03 0.440690E-02 15 -0.15350342 -0.15339661 -0.529426E-03 0.193802E-02 16 -0.15350342 -0.15345001 -0.529426E-03 0.704119E-03 17 -0.15350342 -0.15347672 -0.529426E-03 0.873016E-04 18 -0.15349007 -0.15347672 -0.221073E-03 0.873016E-04 19 -0.15348339 -0.15347672 -0.668886E-04 0.873016E-04 20 -0.15348339 -0.15348005 -0.668886E-04 0.102058E-04 21 -0.15348172 -0.15348005 -0.283416E-04 0.102058E-04 22 -0.15348089 -0.15348005 -0.906793E-05 0.102058E-04 Interval small enough for convergence. BRENT Step XA XB F(XA) F(XB) 0 -0.50000000 3.0000000 -4.16154 1.16171 1 2.2361859 -0.50000000 0.862403E-01 -4.16154 2 2.1761800 -0.50000000 0.349341E-01 -4.16154 3 2.1356996 -0.50000000 0.545632E-02 -4.16154 4 2.1282403 -0.50000000 0.524088E-03 -4.16154 5 2.1274483 -0.50000000 0.996823E-05 -4.16154 6 2.1274330 -0.50000000 0.190397E-07 -4.16154 Function small enough for convergence. MULLER Step XA XB XC F(XA) F(XB) F(XC) 0 3.00000 -0.500000 0.00000 1.16171 -4.16154 5.97647 1 -0.500000 0.00000 -0.312810 -4.16154 5.97647 -2.56997 2 0.00000 -0.312810 -0.186275 5.97647 -2.56997 -0.695481 3 -0.312810 -0.186275 -0.158639 -2.56997 -0.695481 -0.117510 4 -0.186275 -0.158639 -0.153350 -0.695481 -0.117510 0.301335E-02 5 -0.158639 -0.153350 -0.153481 -0.117510 0.301335E-02 -0.336252E-05 6 -0.153350 -0.153481 -0.153480 0.301335E-02 -0.336252E-05 -0.161275E-10 Stepsize small enough for convergence. NEWTON Step X F(X) FP(X) 0 3.0000000 1.16171 1.68657 1 2.3112037 0.161268 1.07147 2 2.1606930 0.231325E-01 0.741569 3 2.1294990 0.134496E-02 0.654013 4 2.1274425 0.622223E-05 0.647955 5 2.1274329 0.136225E-09 0.647927 The function norm is small enough for convergence. NEWTON Step X F(X) FP(X) 0 -0.50000000 -4.16154 6.48698 1 0.14152148 25.1858 263.049 2 0.45775836E-01 9.59021 96.1733 3 -0.53942228E-01 3.13708 42.7976 4 -0.12724278 0.652390 26.7632 5 -0.15161917 0.432095E-01 23.3322 6 -0.15347109 0.217143E-03 23.0983 7 -0.15348049 0.554031E-08 23.0971 The function norm is small enough for convergence. NEWTON Step X F(X) FP(X) 0 0.0000000 5.97647 64.4913 1 -0.92670887E-01 1.68038 33.0197 2 -0.14356109 0.235445 24.3916 3 -0.15321377 0.616505E-02 23.1306 4 -0.15348030 0.445962E-05 23.0971 5 -0.15348049 0.233680E-11 23.0971 The function norm is small enough for convergence. NEWTON Step X F(X) FP(X) 0 2.1274200 -0.837865E-05 0.647889 1 2.1274329 0.247073E-09 0.647927 The function norm is small enough for convergence. REGULA FALSI Step XA XB F(XA) F(XB) 0 -0.50000000 3.0000000 -4.16154 1.16171 1 -0.50000000 2.2361859 -4.16154 0.862403E-01 2 -0.50000000 2.1806346 -4.16154 0.384438E-01 3 -0.50000000 2.1560979 -4.16154 0.197533E-01 4 -0.50000000 2.1435499 -4.16154 0.108204E-01 5 -0.50000000 2.1366943 -4.16154 0.612623E-02 6 -0.50000000 2.1328185 -4.16154 0.353206E-02 7 -0.50000000 2.1305858 -4.16154 0.205746E-02 8 -0.50000000 2.1292859 -4.16154 0.120563E-02 9 -0.50000000 2.1285244 -4.16154 0.708928E-03 10 -0.50000000 2.1280767 -4.16154 0.417706E-03 11 -0.50000000 2.1278129 -4.16154 0.246409E-03 12 -0.50000000 2.1276573 -4.16154 0.145462E-03 13 -0.50000000 2.1275655 -4.16154 0.859055E-04 14 -0.50000000 2.1275112 -4.16154 0.507457E-04 15 -0.50000000 2.1274792 -4.16154 0.299806E-04 16 -0.50000000 2.1274603 -4.16154 0.177141E-04 17 -0.50000000 2.1274491 -4.16154 0.104669E-04 18 -0.50000000 2.1274425 -4.16154 0.618489E-05 19 -0.50000000 2.1274386 -4.16154 0.365471E-05 20 -0.50000000 2.1274363 -4.16154 0.215962E-05 21 -0.50000000 2.1274349 -4.16154 0.127616E-05 22 -0.50000000 2.1274341 -4.16154 0.754112E-06 Function small enough for convergence. SECANT Step X F(X) -1 3.0000000 1.16171 0 -0.50000000 -4.16154 1 2.2361859 0.862403E-01 2 2.1806346 0.384438E-01 3 2.1359535 0.562704E-02 4 2.1282921 0.557740E-03 5 2.1274491 0.104931E-04 6 2.1274330 0.204948E-07 Function small enough for convergence. SECANT Step X F(X) -1 -0.50000000 -4.16154 0 0.0000000 5.97647 1 -0.29475563 -2.35879 2 -0.21134285 -1.15480 3 -0.13133882 0.544056 4 -0.15696005 -0.796156E-01 5 -0.15368933 -0.482085E-02 6 -0.15347852 0.455622E-04 7 -0.15348050 -0.258252E-07 Function small enough for convergence. SECANT Step X F(X) -1 0.0000000 5.97647 0 2.1274200 -0.837865E-05 1 2.1274170 -0.103110E-04 2 2.1274329 0.304060E-09 Function small enough for convergence. Problem number 15 Donovan/Miller/Moreland Pathological Function We seek roots between -10.0000 and 10.0000 Number of known roots = 1 Tabulated solutions: X F(X) 0.0000000 0.0000000 Number of starting points = 2 I XSTART(I), F(XSTART(I)) 1 0.10000000E-01 0.21542193 2 -0.25000000 -0.59179315 BISECTION Step XA XB F(XA) F(XB) 0 -0.25000000 0.10000000E-01 -0.591793 0.215422 1 -0.12000000 0.10000000E-01 -0.486191 0.215422 2 -0.55000000E-01 0.10000000E-01 -0.379147 0.215422 3 -0.22500000E-01 0.10000000E-01 -0.282168 0.215422 4 -0.62500000E-02 0.10000000E-01 -0.184194 0.215422 5 -0.62500000E-02 0.18750000E-02 -0.184194 0.123310 6 -0.21875000E-02 0.18750000E-02 -0.129812 0.123310 7 -0.15625000E-03 0.18750000E-02 -0.538609E-01 0.123310 8 -0.15625000E-03 0.85937500E-03 -0.538609E-01 0.950737E-01 9 -0.15625000E-03 0.35156250E-03 -0.538609E-01 0.705777E-01 10 -0.15625000E-03 0.97656250E-04 -0.538609E-01 0.460504E-01 11 -0.29296875E-04 0.97656250E-04 -0.308277E-01 0.460504E-01 12 -0.29296875E-04 0.34179688E-04 -0.308277E-01 0.324531E-01 13 -0.29296875E-04 0.24414063E-05 -0.308277E-01 0.134652E-01 14 -0.13427734E-04 0.24414063E-05 -0.237685E-01 0.134652E-01 15 -0.54931641E-05 0.24414063E-05 -0.176444E-01 0.134652E-01 16 -0.15258789E-05 0.24414063E-05 -0.115126E-01 0.134652E-01 17 -0.15258789E-05 0.45776367E-06 -0.115126E-01 0.770691E-02 18 -0.53405762E-06 0.45776367E-06 -0.811327E-02 0.770691E-02 Interval small enough for convergence. BRENT Step XA XB F(XA) F(XB) 0 -0.25000000 0.10000000E-01 -0.591793 0.215422 1 -0.59386342E-01 0.10000000E-01 -0.388774 0.215422 2 -0.14739226E-01 0.10000000E-01 -0.245130 0.215422 3 -0.15716958E-02 0.10000000E-01 -0.116267 0.215422 4 0.24845252E-02 -0.15716958E-02 0.135439 -0.116267 5 0.30193073E-03 -0.15716958E-02 0.670866E-01 -0.116267 6 -0.38360517E-03 0.30193073E-03 -0.726599E-01 0.670866E-01 7 -0.27167116E-04 0.30193073E-03 -0.300618E-01 0.670866E-01 8 0.74669528E-04 -0.27167116E-04 0.421096E-01 -0.300618E-01 9 0.15251222E-04 -0.27167116E-04 0.247990E-01 -0.300618E-01 10 -0.39233787E-05 0.15251222E-04 -0.157720E-01 0.247990E-01 11 0.35307508E-05 -0.39233787E-05 0.152273E-01 -0.157720E-01 12 -0.13082208E-06 0.35307508E-05 -0.507645E-02 0.152273E-01 13 0.78466481E-06 -0.13082208E-06 0.922348E-02 -0.507645E-02 Interval small enough for convergence. NEWTON Step X F(X) FP(X) 0 0.10000000E-01 0.215422 7.17642 1 -0.20018011E-01 -0.271414 4.50864 2 0.40180759E-01 0.341957 2.80934 3 -0.81540628E-01 -0.430762 1.69068 4 0.17324550 0.540986 0.853438 5 -0.46064446 -0.624646 -0.123471 6 -5.5197083 -0.103652E-12 -0.113800E-11 The function norm is small enough for convergence. NEWTON Step X F(X) FP(X) 0 -0.25000000 -0.591793 0.493161 1 0.95000000 0.398679 -0.617603 2 1.5955266 0.916324E-01 -0.273260 3 1.9308567 0.299302E-01 -0.110415 4 2.2019271 0.102000E-01 -0.433750E-01 5 2.4370845 0.354419E-02 -0.167902E-01 6 2.6481710 0.124554E-02 -0.644002E-02 7 2.8415771 0.441011E-03 -0.245460E-02 8 3.0212442 0.156985E-03 -0.931260E-03 9 3.1898169 0.561055E-04 -0.352069E-03 10 3.3491760 0.201144E-04 -0.132731E-03 11 3.5007182 0.722928E-05 -0.499270E-04 12 3.6455152 0.260360E-05 -0.187449E-04 13 3.7844120 0.939288E-06 -0.702657E-05 The function norm is small enough for convergence. REGULA FALSI Step XA XB F(XA) F(XB) 0 -0.25000000 0.10000000E-01 -0.591793 0.215422 1 -0.59386342E-01 0.10000000E-01 -0.388774 0.215422 2 -0.14739226E-01 0.10000000E-01 -0.245130 0.215422 3 -0.15716958E-02 0.10000000E-01 -0.116267 0.215422 4 -0.15716958E-02 0.24845252E-02 -0.116267 0.135439 5 -0.15716958E-02 0.30193073E-03 -0.116267 0.670866E-01 6 -0.38360517E-03 0.30193073E-03 -0.726599E-01 0.670866E-01 7 -0.27167116E-04 0.30193073E-03 -0.300618E-01 0.670866E-01 8 -0.27167116E-04 0.74669528E-04 -0.300618E-01 0.421096E-01 9 -0.27167116E-04 0.15251222E-04 -0.300618E-01 0.247990E-01 10 -0.39233787E-05 0.15251222E-04 -0.157720E-01 0.247990E-01 11 -0.39233787E-05 0.35307508E-05 -0.157720E-01 0.152273E-01 12 -0.13082208E-06 0.35307508E-05 -0.507645E-02 0.152273E-01 13 -0.13082208E-06 0.78466481E-06 -0.507645E-02 0.922348E-02 Interval small enough for convergence. SECANT Step X F(X) -1 0.10000000E-01 0.215422 0 -0.25000000 -0.591793 1 -0.59386342E-01 -0.388774 2 0.30563162 0.613524 3 0.82197767E-01 0.431869 4 -0.44899773 -0.625933 5 -0.13467355 -0.503366 6 1.1562114 0.275700 7 0.69938631 0.544262 8 1.6251790 0.837990E-01 9 1.7936628 0.486807E-01 10 2.0272134 0.207743E-01 11 2.2010746 0.102370E-01 12 2.3699812 0.484803E-02 13 2.5219332 0.235361E-02 14 2.6653076 0.113958E-02 15 2.7998907 0.555193E-03 16 2.9277496 0.270933E-03 17 3.0496138 0.132560E-03 18 3.1663593 0.649666E-04 19 3.2785673 0.318905E-04 20 3.3867534 0.156745E-04 21 3.4913268 0.771301E-05 22 3.5926363 0.379912E-05 23 3.6909752 0.187294E-05 24 3.7865959 0.924063E-06 Function small enough for convergence. Problem number 16 Kepler's Eccentric Anomaly Equation, in degrees We seek roots between -175.000 and 185.000 Number of known roots = 0 Tabulated solutions: X F(X) Number of starting points = 3 I XSTART(I), F(XSTART(I)) 1 0.0000000 -0.87266463E-01 2 5.0000000 -0.69724594E-01 3 185.00000 3.2113172 BISECTION Step XA XB F(XA) F(XB) 0 0.0000000 185.00000 -0.872665E-01 3.21132 1 0.0000000 92.500000 -0.872665E-01 0.727925 2 0.0000000 46.250000 -0.872665E-01 0.142057 3 0.0000000 23.125000 -0.872665E-01 0.215019E-02 4 11.562500 23.125000 -0.458122E-01 0.215019E-02 5 17.343750 23.125000 -0.230440E-01 0.215019E-02 6 20.234375 23.125000 -0.107990E-01 0.215019E-02 7 21.679688 23.125000 -0.441841E-02 0.215019E-02 8 22.402344 23.125000 -0.115836E-02 0.215019E-02 9 22.402344 22.763672 -0.115836E-02 0.489757E-03 10 22.583008 22.763672 -0.335829E-03 0.489757E-03 11 22.583008 22.673340 -0.335829E-03 0.765808E-04 12 22.628174 22.673340 -0.129720E-03 0.765808E-04 13 22.650757 22.673340 -0.265934E-04 0.765808E-04 14 22.650757 22.662048 -0.265934E-04 0.249877E-04 15 22.656403 22.662048 -0.804366E-06 0.249877E-04 Function small enough for convergence. BRENT Step XA XB F(XA) F(XB) 0 185.00000 0.0000000 3.21132 -0.872665E-01 1 4.8943113 185.00000 -0.700990E-01 3.21132 2 24.452096 4.8943113 0.835729E-02 -0.700990E-01 3 22.368771 24.452096 -0.131088E-02 0.835729E-02 4 22.651243 24.452096 -0.243743E-04 0.835729E-02 5 22.656579 22.651243 0.908424E-09 -0.243743E-04 Function small enough for convergence. MULLER Step XA XB XC F(XA) F(XB) F(XC) 0 0.00000 5.00000 185.000 -0.872665E-01 -0.697246E-01 3.21132 1 5.00000 0.00000 18.9091 -0.697246E-01 -0.872665E-01 -0.164947E-01 2 5.00000 18.9091 22.9042 -0.697246E-01 -0.164947E-01 0.113413E-02 3 18.9091 22.9042 22.6541 -0.164947E-01 0.113413E-02 -0.111682E-04 4 22.9042 22.6541 22.6566 0.113413E-02 -0.111682E-04 -0.149320E-08 Function small enough for convergence. NEWTON Step X F(X) FP(X) 0 0.0000000 -0.872665E-01 0.349066E-02 1 25.000000 0.109712E-01 0.479885E-02 2 22.713776 0.261441E-03 0.457353E-02 3 22.656612 0.153620E-06 0.456815E-02 The function norm is small enough for convergence. NEWTON Step X F(X) FP(X) 0 5.0000000 -0.697246E-01 0.354379E-02 1 24.675145 0.941773E-02 0.476560E-02 2 22.698955 0.193665E-03 0.457213E-02 3 22.656597 0.843112E-07 0.456815E-02 The function norm is small enough for convergence. NEWTON Step X F(X) FP(X) 0 185.00000 3.21132 0.313628E-01 1 82.607426 0.561155 0.156568E-01 2 46.766372 0.146107 0.788924E-02 3 28.246548 0.271155E-01 0.515334E-02 4 22.984809 0.150449E-02 0.459917E-02 5 22.657688 0.506855E-05 0.456826E-02 6 22.656579 0.577814E-10 0.456815E-02 The function norm is small enough for convergence. REGULA FALSI Step XA XB F(XA) F(XB) 0 0.0000000 185.00000 -0.872665E-01 3.21132 1 4.8943113 185.00000 -0.700990E-01 3.21132 2 8.7418059 185.00000 -0.562788E-01 3.21132 3 11.777554 185.00000 -0.449994E-01 3.21132 4 14.171335 185.00000 -0.357879E-01 3.21132 5 16.054119 185.00000 -0.283054E-01 3.21132 6 17.530241 185.00000 -0.222733E-01 3.21132 7 18.683792 185.00000 -0.174488E-01 3.21132 8 19.582593 185.00000 -0.136180E-01 3.21132 9 20.281105 185.00000 -0.105955E-01 3.21132 10 20.822794 185.00000 -0.822322E-02 3.21132 11 21.242129 185.00000 -0.636937E-02 3.21132 12 21.566285 185.00000 -0.492568E-02 3.21132 13 21.816584 185.00000 -0.380449E-02 3.21132 14 22.009681 185.00000 -0.293566E-02 3.21132 15 22.158545 185.00000 -0.226353E-02 3.21132 16 22.273244 185.00000 -0.174427E-02 3.21132 17 22.361584 185.00000 -0.134351E-02 3.21132 18 22.429598 185.00000 -0.103447E-02 3.21132 19 22.481950 185.00000 -0.796301E-03 3.21132 20 22.522239 185.00000 -0.612836E-03 3.21132 21 22.553240 185.00000 -0.471565E-03 3.21132 22 22.577091 185.00000 -0.362815E-03 3.21132 23 22.595440 185.00000 -0.279117E-03 3.21132 24 22.609554 185.00000 -0.214712E-03 3.21132 25 22.620411 185.00000 -0.165158E-03 3.21132 Took maximum number of steps without convergence. SECANT Step X F(X) -1 0.0000000 -0.872665E-01 0 5.0000000 -0.697246E-01 1 24.873765 0.103663E-01 2 22.301475 -0.161628E-02 3 22.648441 -0.371725E-04 4 22.656608 0.135454E-06 Function small enough for convergence. SECANT Step X F(X) -1 5.0000000 -0.697246E-01 0 185.00000 3.21132 1 8.8251347 -0.559743E-01 2 11.843311 -0.447504E-01 3 23.877051 0.564640E-02 4 22.528805 -0.582924E-03 5 22.654970 -0.734664E-05 6 22.656581 0.964046E-08 Function small enough for convergence. Problem number 17 The Wallis example, x^3-2x-5=0 We seek roots between 2.00000 and 3.00000 Number of known roots = 1 Tabulated solutions: X F(X) 2.0945515 -0.88817842E-15 Number of starting points = 2 I XSTART(I), F(XSTART(I)) 1 2.0000000 -1.0000000 2 3.0000000 16.000000 BISECTION Step XA XB F(XA) F(XB) 0 2.0000000 3.0000000 -1.00000 16.0000 1 2.0000000 2.5000000 -1.00000 5.62500 2 2.0000000 2.2500000 -1.00000 1.89063 3 2.0000000 2.1250000 -1.00000 0.345703 4 2.0625000 2.1250000 -0.351318 0.345703 5 2.0937500 2.1250000 -0.894165E-02 0.345703 6 2.0937500 2.1093750 -0.894165E-02 0.166836 7 2.0937500 2.1015625 -0.894165E-02 0.785623E-01 8 2.0937500 2.0976563 -0.894165E-02 0.347143E-01 9 2.0937500 2.0957031 -0.894165E-02 0.128623E-01 10 2.0937500 2.0947266 -0.894165E-02 0.195435E-02 11 2.0942383 2.0947266 -0.349515E-02 0.195435E-02 12 2.0944824 2.0947266 -0.770775E-03 0.195435E-02 13 2.0944824 2.0946045 -0.770775E-03 0.591693E-03 14 2.0945435 2.0946045 -0.895647E-04 0.591693E-03 15 2.0945435 2.0945740 -0.895647E-04 0.251058E-03 16 2.0945435 2.0945587 -0.895647E-04 0.807453E-04 17 2.0945511 2.0945587 -0.441007E-05 0.807453E-04 18 2.0945511 2.0945549 -0.441007E-05 0.381675E-04 19 2.0945511 2.0945530 -0.441007E-05 0.168787E-04 20 2.0945511 2.0945520 -0.441007E-05 0.623431E-05 Interval small enough for convergence. BRENT Step XA XB F(XA) F(XB) 0 3.0000000 2.0000000 16.0000 -1.00000 1 2.0588235 3.0000000 -0.390800 16.0000 2 2.0956589 2.0588235 0.123685E-01 -0.390800 3 2.0945289 2.0956589 -0.252138E-03 0.123685E-01 4 2.0945515 2.0956589 -0.157134E-06 0.123685E-01 Function small enough for convergence. NEWTON Step X F(X) FP(X) 0 2.0000000 -1.00000 10.0000 1 2.1000000 0.610000E-01 11.2300 2 2.0945681 0.185723E-03 11.1616 3 2.0945515 0.173976E-08 11.1614 The function norm is small enough for convergence. NEWTON Step X F(X) FP(X) 0 3.0000000 16.0000 25.0000 1 2.3600000 3.42426 14.7088 2 2.1271968 0.371100 11.5749 3 2.0951360 0.652663E-02 11.1688 4 2.0945517 0.214614E-05 11.1614 5 2.0945515 0.232703E-12 11.1614 The function norm is small enough for convergence. REGULA FALSI Step XA XB F(XA) F(XB) 0 2.0000000 3.0000000 -1.00000 16.0000 1 2.0588235 3.0000000 -0.390800 16.0000 2 2.0812637 3.0000000 -0.147204 16.0000 3 2.0896392 3.0000000 -0.546765E-01 16.0000 4 2.0927396 3.0000000 -0.202029E-01 16.0000 5 2.0938837 3.0000000 -0.745051E-02 16.0000 6 2.0943055 3.0000000 -0.274567E-02 16.0000 7 2.0944608 3.0000000 -0.101157E-02 16.0000 8 2.0945181 3.0000000 -0.372653E-03 16.0000 9 2.0945392 3.0000000 -0.137276E-03 16.0000 10 2.0945470 3.0000000 -0.505686E-04 16.0000 11 2.0945498 3.0000000 -0.186279E-04 16.0000 12 2.0945509 3.0000000 -0.686195E-05 16.0000 13 2.0945513 3.0000000 -0.252773E-05 16.0000 14 2.0945514 3.0000000 -0.931134E-06 16.0000 Function small enough for convergence. SECANT Step X F(X) -1 2.0000000 -1.00000 0 3.0000000 16.0000 1 2.0588235 -0.390800 2 2.0812637 -0.147204 3 2.0948241 0.304380E-02 4 2.0945494 -0.228866E-04 5 2.0945515 -0.351281E-08 Function small enough for convergence. Problem number 18 10^14 * (x-1)^7, written term by term. We seek roots between 0.988000 and 1.01200 Number of known roots = 1 Tabulated solutions: X F(X) 1.0000000 0.0000000 Number of starting points = 2 I XSTART(I), F(XSTART(I)) 1 0.99000000 -1.4210855 2 1.0130000 6.2172489 BISECTION Step XA XB F(XA) F(XB) 0 0.99000000 1.0130000 -1.42109 6.21725 1 0.99000000 1.0015000 -1.42109 0.00000 Function small enough for convergence. BRENT Step XA XB F(XA) F(XB) 0 1.0130000 0.99000000 6.21725 -1.42109 1 0.99427907 0.99000000 0.266454 -1.42109 2 0.99360343 0.99427907 -0.444089 0.266454 3 0.99402570 0.99427907 -0.177636 0.266454 4 0.99412705 0.99402570 0.266454 -0.177636 5 0.99406624 0.99412705 -0.888178 0.266454 6 0.99411302 0.99412705 -0.177636 0.266454 7 0.99411863 0.99411302 0.355271 -0.177636 8 0.99411551 0.99411863 -0.799361 0.355271 Interval small enough for convergence. NEWTON Step X F(X) FP(X) 0 0.99000000 -1.42109 699.174 1 0.99203252 -0.888178E-01 179.767 2 0.99252659 -0.355271 124.345 3 0.99538373 -0.266454 7.81597 4 1.0294746 1933.48 458974. The iterate X = 1.02947 has left the region [XMIN,XMAX]. NEWTON Step X F(X) FP(X) 0 1.0130000 6.21725 3377.92 The iterate X = 1.01300 has left the region [XMIN,XMAX]. REGULA FALSI Step XA XB F(XA) F(XB) 0 0.99000000 1.0130000 -1.42109 6.21725 1 0.99000000 0.99427907 -1.42109 0.266454 2 0.99360343 0.99427907 -0.444089 0.266454 3 0.99360343 0.99402570 -0.444089 0.177636 4 0.99390505 0.99402570 -0.888178E-01 0.177636 5 0.99394527 0.99402570 -0.888178E-01 0.177636 6 0.99394527 0.99397208 -0.888178E-01 0.888178E-01 7 0.99394527 0.99395868 -0.888178E-01 0.444089 8 0.99394750 0.99395868 -0.888178E-01 0.444089 9 0.99394750 0.99394937 -0.888178E-01 0.355271 10 0.99394788 0.99394937 -0.888178 0.355271 11 0.99394788 0.99394894 -0.888178 0.00000 Function small enough for convergence. SECANT Step X F(X) -1 0.99000000 -1.42109 0 1.0130000 6.21725 Iterate has left the region [XMIN,XMAX]. Problem number 19 The jumping cosine. We seek roots between 0.00000 and 1.00000 Number of known roots = 1 Tabulated solutions: X F(X) 0.33186603 0.70776718E-14 Number of starting points = 3 I XSTART(I), F(XSTART(I)) 1 0.0000000 5.0000000 2 1.0000000 -3.1376811 3 0.50000000 -3.0350340 BISECTION Step XA XB F(XA) F(XB) 0 1.0000000 0.0000000 -3.13768 5.00000 1 0.50000000 0.0000000 -3.03503 5.00000 2 0.50000000 0.25000000 -3.03503 4.98958 3 0.37500000 0.25000000 -2.71136 4.98958 4 0.37500000 0.31250000 -2.71136 3.47923 5 0.34375000 0.31250000 -2.34926 3.47923 6 0.34375000 0.32812500 -2.34926 0.872882 7 0.33593750 0.32812500 -0.922331 0.872882 8 0.33203125 0.32812500 -0.384975E-01 0.872882 9 0.33203125 0.33007813 -0.384975E-01 0.418288 10 0.33203125 0.33105469 -0.384975E-01 0.189594 11 0.33203125 0.33154297 -0.384975E-01 0.754015E-01 12 0.33203125 0.33178711 -0.384975E-01 0.184063E-01 13 0.33190918 0.33178711 -0.100581E-01 0.184063E-01 14 0.33190918 0.33184814 -0.100581E-01 0.417113E-02 15 0.33187866 0.33184814 -0.294424E-02 0.417113E-02 16 0.33187866 0.33186340 -0.294424E-02 0.613256E-03 17 0.33187103 0.33186340 -0.116554E-02 0.613256E-03 18 0.33186722 0.33186340 -0.276155E-03 0.613256E-03 19 0.33186722 0.33186531 -0.276155E-03 0.168548E-03 20 0.33186626 0.33186531 -0.538042E-04 0.168548E-03 Interval small enough for convergence. BRENT Step XA XB F(XA) F(XB) 0 1.0000000 0.0000000 -3.13768 5.00000 1 0.61442565 0.0000000 -3.81949 5.00000 2 0.30721282 0.61442565 3.69718 -3.81949 3 0.45831981 0.30721282 -4.27529 3.69718 4 0.37728771 0.30721282 -2.75162 3.69718 5 0.34738767 0.30721282 -2.77965 3.69718 6 0.32730025 0.34738767 1.06197 -2.77965 7 0.33285316 0.32730025 -0.229163 1.06197 8 0.33186758 0.32730025 -0.359493E-03 1.06197 9 0.33186603 0.33186758 0.142922E-05 -0.359493E-03 Interval small enough for convergence. MULLER Step XA XB XC F(XA) F(XB) F(XC) 0 0.00000 1.00000 0.500000 5.00000 -3.13768 -3.03503 1 0.00000 0.500000 0.249436 5.00000 -3.03503 4.98068 2 0.500000 0.249436 0.430283 -3.03503 4.98068 -3.42143 3 0.249436 0.430283 0.321604 4.98068 -3.42143 2.26043 4 0.430283 0.321604 0.369329 -3.42143 2.26043 -2.77259 5 0.321604 0.369329 0.338706 2.26043 -2.77259 -1.49440 6 0.321604 0.338706 0.330663 2.26043 -1.49440 0.281298 7 0.338706 0.330663 0.331942 -1.49440 0.281298 -0.178101E-01 8 0.330663 0.331942 0.331866 0.281298 -0.178101E-01 0.123931E-03 9 0.331942 0.331866 0.331866 -0.178101E-01 0.123931E-03 -0.998992E-08 Stepsize small enough for convergence. NEWTON Step X F(X) FP(X) 0 0.0000000 5.00000 0.503719E-41 1 -0.99261741E+42 4.68471 -72.8813 The iterate X = -0.992617E+42 has left the region [XMIN,XMAX]. NEWTON Step X F(X) FP(X) 0 1.0000000 -3.13768 50.6366 1 1.0619647 -3.18477 57.9143 The iterate X = 1.06196 has left the region [XMIN,XMAX]. NEWTON Step X F(X) FP(X) 0 0.50000000 -3.03503 26.2375 1 0.61567549 -3.69828 95.3398 2 0.65446605 -4.86440 -50.2805 3 0.55772072 -3.28670 70.0855 4 0.60461624 -4.71696 69.7113 5 0.67228042 -4.31096 95.0424 6 0.71763868 -4.88103 -47.3062 7 0.61445910 -3.81620 98.2963 8 0.65328251 -4.79898 -60.1354 9 0.57347960 -3.30279 -71.6863 10 0.52740683 -4.78606 -61.8154 11 0.44998182 -3.47313 -84.9941 12 0.40911863 -4.99226 7.88028 13 1.0426310 -4.83064 55.6810 The iterate X = 1.04263 has left the region [XMIN,XMAX]. REGULA FALSI Step XA XB F(XA) F(XB) 0 1.0000000 0.0000000 -3.13768 5.00000 1 0.61442565 0.0000000 -3.81949 5.00000 2 0.34833412 0.0000000 -2.86420 5.00000 3 0.34833412 0.22146835 -2.86420 3.01209 4 0.34833412 0.28649767 -2.86420 2.88199 5 0.34833412 0.31751165 -2.86420 2.93611 6 0.33311394 0.31751165 -0.289292 2.93611 7 0.33311394 0.33171455 -0.289292 0.353374E-01 8 0.33186688 0.33171455 -0.196929E-03 0.353374E-01 9 0.33186603 0.33171455 -0.100210E-06 0.353374E-01 Function small enough for convergence. SECANT Step X F(X) -1 0.0000000 5.00000 0 1.0000000 -3.13768 1 0.61442565 -3.81949 2 2.7744193 -3.44445 Iterate has left the region [XMIN,XMAX]. SECANT Step X F(X) -1 1.0000000 -3.13768 0 0.50000000 -3.03503 1 -14.283819 3.49615 Iterate has left the region [XMIN,XMAX]. TEST_ZERO_PRB Normal end of execution. 15 January 2013 8:29:27.692 AM