21 March 2018 10:58:50.587 AM TEST_ZERO_TEST FORTRAN90 version Test the TEST_ZERO library. TEST01 Try every test problem. 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 available 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 I X F(X) 1 -1.8954943 0.0000000 2 0.0000000 0.0000000 3 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 X F(X) FP(X) 0 1.5707963 0.214602 -0.500000 The iterate X = 1.57080 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 3.1415927 -1.57080 -1.50000 The iterate X = 3.14159 has left the region [XMIN,XMAX]. 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 X F(X) -1 1.5707963 0.214602 0 3.1415927 -1.57080 Iterate has left the region [XMIN,XMAX]. Problem number 2 F(X) = 2 * X - EXP ( - X ) We seek roots between -10.0000 and 100.000 Number of known roots = 1 I X F(X) 1 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 0.35351562 -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 X F(X) FP(X) 0 0.0000000 -1.00000 3.00000 The iterate X = 0.00000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 1.0000000 1.63212 2.36788 The iterate X = 1.00000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 -5.0000000 -158.413 150.413 The iterate X = -5.00000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 10.000000 20.0000 2.00005 The iterate X = 10.0000 has left the region [XMIN,XMAX]. 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 X F(X) -1 0.0000000 -1.00000 0 1.0000000 1.63212 Iterate has left the region [XMIN,XMAX]. SECANT X F(X) -1 1.0000000 1.63212 0 -5.0000000 -158.413 Iterate has left the region [XMIN,XMAX]. SECANT X F(X) -1 -5.0000000 -158.413 0 10.000000 20.0000 Iterate has left the region [XMIN,XMAX]. Problem number 3 F(X) = X * EXP ( - X ) We seek roots between -10.0000 and 100.000 Number of known roots = 1 I X F(X) 1 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 -0.24414062E-03 0.48828125E-03 -0.244200E-03 0.488043E-03 12 -0.24414062E-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 X F(X) FP(X) 0 -1.0000000 -2.71828 5.43656 The iterate X = -1.00000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 0.50000000 0.303265 0.303265 The iterate X = 0.500000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 2.0000000 0.270671 -0.135335 The iterate X = 2.00000 has left the region [XMIN,XMAX]. 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 X F(X) -1 -1.0000000 -2.71828 0 0.50000000 0.303265 Iterate has left the region [XMIN,XMAX]. SECANT X F(X) -1 0.50000000 0.303265 0 2.0000000 0.270671 Iterate has left the region [XMIN,XMAX]. Problem number 4 F(X) = EXP ( X ) - 1 / ( 100 * X * X ) We seek roots between 0.100000E-04 and 20.0000 Number of known roots = 1 I X F(X) 1 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 X F(X) FP(X) 0 0.30000000E-01 -10.0807 741.771 The iterate X = 0.300000E-01 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 1.0000000 2.70828 2.73828 The iterate X = 1.00000 has left the region [XMIN,XMAX]. 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 X F(X) -1 0.30000000E-01 -10.0807 0 1.0000000 2.70828 Iterate has left the region [XMIN,XMAX]. Problem number 5 F(X) = ( X + 3 ) * ( X - 1 ) * ( X - 1 ) We seek roots between -1000.00 and 1000.00 Number of known roots = 3 I X F(X) 1 -3.0000000 0.0000000 2 1.0000000 0.0000000 3 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 -4.51562 9.37500 3 -3.2500000 -2.3750000 -4.51562 7.11914 4 -3.2500000 -2.8125000 -4.51562 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 -3.0039062 -2.9765625 -0.626221E-01 0.370618 9 -3.0039062 -2.9902344 -0.626221E-01 0.155488 10 -3.0039062 -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 X F(X) FP(X) 0 2.0000000 5.00000 11.0000 The iterate X = 2.00000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 -5.0000000 -72.0000 60.0000 The iterate X = -5.00000 has left the region [XMIN,XMAX]. 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 X F(X) -1 2.0000000 5.00000 0 -5.0000000 -72.0000 Iterate has left the region [XMIN,XMAX]. 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 I X F(X) 1 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 X F(X) FP(X) 0 0.20000000E-03 -0.999800 -0.125000E+10 The iterate X = 0.200000E-03 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 2.0000000 5.38656 7.39156 The iterate X = 2.00000 has left the region [XMIN,XMAX]. 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 X F(X) -1 0.20000000E-03 -0.999800 0 2.0000000 5.38656 Iterate has left the region [XMIN,XMAX]. 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 I X F(X) 1 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 -2.9101562 1.0000000 -24.6461 1.00000 9 -0.95507812 1.0000000 -0.871198 1.00000 10 -0.95507812 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 X F(X) FP(X) 0 1.0000000 1.00000 3.00000 The iterate X = 1.00000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 -1000.0000 -0.100000E+10 0.300000E+07 The iterate X = -1000.00 has left the region [XMIN,XMAX]. 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 X F(X) -1 1.0000000 1.00000 0 -1000.0000 -0.100000E+10 Iterate has left the region [XMIN,XMAX]. Problem number 8 F(X) = COS(X) - X We seek roots between -10.0000 and 10.0000 Number of known roots = 1 I X F(X) 1 0.73908513 0.0000000 Number of starting points = 3 I XSTART(I), F(XSTART(I)) 1 1.0000000 -0.45969769 2 0.50000000 0.37758256 3 -1.6000000 1.5708005 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. MULLER Step XA XB XC F(XA) F(XB) F(XC) 0 1.00000 0.500000 -1.60000 -0.459698 0.377583 1.57080 1 0.500000 -1.60000 -3.17664 0.377583 1.57080 2.17725 2 0.500000 -1.60000 1.03943 0.377583 1.57080 -0.532715 3 0.500000 1.03943 0.741835 0.377583 -0.532715 -0.460571E-02 4 0.500000 0.741835 0.739072 0.377583 -0.460571E-02 0.225856E-04 5 0.741835 0.739072 0.739085 -0.460571E-02 0.225856E-04 -0.929012E-09 Function small enough for convergence. NEWTON X F(X) FP(X) 0 1.0000000 -0.459698 -1.84147 The iterate X = 1.00000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 0.50000000 0.377583 -1.47943 The iterate X = 0.500000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 -1.6000000 1.57080 -0.426397E-03 The iterate X = -1.60000 has left the region [XMIN,XMAX]. 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 X F(X) -1 1.0000000 -0.459698 0 0.50000000 0.377583 Iterate has left the region [XMIN,XMAX]. SECANT X F(X) -1 0.50000000 0.377583 0 -1.6000000 1.57080 Iterate has left the region [XMIN,XMAX]. Problem number 9 The Newton Baffler We seek roots between -4.00000 and 16.0000 Number of known roots = 1 I X F(X) 1 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 -0.195312E-02 0.390625E-02 12 6.2490234 6.2504883 -0.195312E-02 0.976562E-03 13 6.2497559 6.2504883 -0.488281E-03 0.976562E-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 X F(X) FP(X) 0 11.250000 4.06250 0.750000 The iterate X = 11.2500 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 5.2500000 -1.06250 0.750000 The iterate X = 5.25000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 6.3500000 0.200000 2.00000 The iterate X = 6.35000 has left the region [XMIN,XMAX]. 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 X F(X) -1 11.250000 4.06250 0 5.2500000 -1.06250 Iterate has left the region [XMIN,XMAX]. SECANT X F(X) -1 5.2500000 -1.06250 0 6.3500000 0.200000 Iterate has left the region [XMIN,XMAX]. Problem number 10 The Repeller We seek roots between -10.0000 and 10.0000 Number of known roots = 1 I X F(X) 1 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 X F(X) FP(X) 0 1.0000000 0.198020 -0.970493E-02 The iterate X = 1.00000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 -0.14000000 -0.945946 -0.109569 The iterate X = -0.140000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 0.41000000E-01 0.701995 0.609693 The iterate X = 0.410000E-01 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 X F(X) -1 1.0000000 0.198020 0 -0.14000000 -0.945946 Iterate has left the region [XMIN,XMAX]. SECANT X F(X) -1 -0.14000000 -0.945946 0 0.41000000E-01 0.701995 Iterate has left the region [XMIN,XMAX]. Problem number 11 The Pinhead We seek roots between 0.00000 and 10.0000 Number of known roots = 2 I X F(X) 1 -2.0000000 0.0000000 2 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 1.9570312 -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 X F(X) FP(X) 0 0.25000000 255.897 -4094.69 The iterate X = 0.250000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 5.0000000 -0.609000E-01 -0.128000E-02 The iterate X = 5.00000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 1.1000000 0.620513 -2.48368 The iterate X = 1.10000 has left the region [XMIN,XMAX]. 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 X F(X) -1 0.25000000 255.897 0 5.0000000 -0.609000E-01 Iterate has left the region [XMIN,XMAX]. SECANT X F(X) -1 5.0000000 -0.609000E-01 0 1.1000000 0.620513 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 I X F(X) 1 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 X F(X) FP(X) 0 2.0000000 367.879 1103.64 The iterate X = 2.00000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 0.50000000 -9.15782 164.841 The iterate X = 0.500000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 4.0000000 2684.52 1093.69 The iterate X = 4.00000 has left the region [XMIN,XMAX]. 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 X F(X) -1 2.0000000 367.879 0 0.50000000 -9.15782 Iterate has left the region [XMIN,XMAX]. SECANT X F(X) -1 0.50000000 -9.15782 0 4.0000000 2684.52 Iterate has left the region [XMIN,XMAX]. 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 I X F(X) 1 100.00000 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 -0.29101562E+09 0.10000000E+09 -0.291016E-02 0.999999E-03 9 -95507812. 0.10000000E+09 -0.955079E-03 0.999999E-03 10 -95507812. 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 X F(X) FP(X) 0 0.10000000E+09 0.999999E-03 0.100000E-10 The iterate X = 0.100000E+09 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 0.10000001E+09 0.999999E-03 0.100000E-10 The iterate X = 0.100000E+09 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 -0.10000000E+12 -1.00000 0.100000E-10 The iterate X = -0.100000E+12 has left the region [XMIN,XMAX]. 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 X F(X) -1 0.10000000E+09 0.999999E-03 0 0.10000001E+09 0.999999E-03 Iterate has left the region [XMIN,XMAX]. SECANT X F(X) -1 0.10000001E+09 0.999999E-03 0 -0.10000000E+12 -1.00000 Iterate has left the region [XMIN,XMAX]. 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 I X F(X) 1 -0.15348049 0.88817842E-15 2 1.8190324 -0.88817842E-15 3 2.1274329 -0.88817842E-15 Number of starting points = 3 I XSTART(I), F(XSTART(I)) 1 3.0000000 1.1617054 2 -0.50000000 -4.1615385 3 0.0000000 5.9764706 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 -0.15820312 -0.14453125 -0.107698 0.211845 9 -0.15820312 -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 X F(X) FP(X) 0 3.0000000 1.16171 1.68657 The iterate X = 3.00000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 -0.50000000 -4.16154 6.48698 The iterate X = -0.500000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 0.0000000 5.97647 64.4913 The iterate X = 0.00000 has left the region [XMIN,XMAX]. 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 X F(X) -1 3.0000000 1.16171 0 -0.50000000 -4.16154 Iterate has left the region [XMIN,XMAX]. SECANT X F(X) -1 -0.50000000 -4.16154 0 0.0000000 5.97647 Iterate has left the region [XMIN,XMAX]. Problem number 15 Donovan/Miller/Moreland Pathological Function We seek roots between -10.0000 and 10.0000 Number of known roots = 1 I X F(X) 1 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 X F(X) FP(X) 0 0.10000000E-01 0.215422 7.17642 The iterate X = 0.100000E-01 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 -0.25000000 -0.591793 0.493161 The iterate X = -0.250000 has left the region [XMIN,XMAX]. 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 X F(X) -1 0.10000000E-01 0.215422 0 -0.25000000 -0.591793 Iterate has left the region [XMIN,XMAX]. Problem number 16 Kepler's Eccentric Anomaly Equation, in degrees We seek roots between -175.000 and 185.000 Number of known roots = 0 I 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 X F(X) FP(X) 0 0.0000000 -0.872665E-01 0.349066E-02 The iterate X = 0.00000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 5.0000000 -0.697246E-01 0.354379E-02 The iterate X = 5.00000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 185.00000 3.21132 0.313628E-01 The iterate X = 185.000 has left the region [XMIN,XMAX]. 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 X F(X) -1 0.0000000 -0.872665E-01 0 5.0000000 -0.697246E-01 Iterate has left the region [XMIN,XMAX]. SECANT X F(X) -1 5.0000000 -0.697246E-01 0 185.00000 3.21132 Iterate has left the region [XMIN,XMAX]. 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 I X F(X) 1 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 1.89062 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 2.0976562 -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 X F(X) FP(X) 0 2.0000000 -1.00000 10.0000 The iterate X = 2.00000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 3.0000000 16.0000 25.0000 The iterate X = 3.00000 has left the region [XMIN,XMAX]. 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 X F(X) -1 2.0000000 -1.00000 0 3.0000000 16.0000 Iterate has left the region [XMIN,XMAX]. 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 I X F(X) 1 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 1.0130000 -0.888178E-01 6.21725 2 0.99456032 1.0130000 -0.355271 6.21725 3 1.0037802 1.0130000 -0.532907 6.21725 4 1.0083901 1.0037802 0.888178 -0.532907 5 1.0055089 1.0037802 0.177636 -0.532907 6 1.0050767 1.0037802 0.00000 -0.532907 Function small enough for convergence. NEWTON X F(X) FP(X) 0 0.99000000 -1.42109 699.174 The iterate X = 0.990000 has left the region [XMIN,XMAX]. NEWTON 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 0.99427907 1.0130000 -0.888178E-01 6.21725 2 0.99454274 1.0130000 -0.621725 6.21725 3 0.99454274 0.99622068 -0.621725 0.00000 Function small enough for convergence. SECANT 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 I X F(X) 1 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 0.33007812 -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 X F(X) FP(X) 0 0.0000000 5.00000 0.503719E-41 The iterate X = 0.00000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 1.0000000 -3.13768 50.6366 The iterate X = 1.00000 has left the region [XMIN,XMAX]. NEWTON X F(X) FP(X) 0 0.50000000 -3.03503 26.2375 The iterate X = 0.500000 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 X F(X) -1 0.0000000 5.00000 0 1.0000000 -3.13768 Iterate has left the region [XMIN,XMAX]. SECANT X F(X) -1 1.0000000 -3.13768 0 0.50000000 -3.03503 Iterate has left the region [XMIN,XMAX]. TEST_ZERO_TEST Normal end of execution. 21 March 2018 10:58:50.590 AM