25 March 2017 10:05:30.847 AM PPPACK_PRB FORTRAN77 version Test the PPPACK library. TEST01 n max.error decay exp. 2 0.9615E+00 0.00 4 0.7070E+00 -0.44 6 0.4327E+00 -1.21 8 0.2474E+00 -1.94 10 0.2994E+00 0.86 12 0.5567E+00 3.40 14 0.1069E+01 4.23 16 0.2099E+01 5.05 18 0.4214E+01 5.92 20 0.8573E+01 6.74 TEST02 n max.error decay exp. 2 0.9246E+00 0.00 4 0.5407E+00 -0.77 6 0.2500E+00 -1.90 8 0.1141E+00 -2.73 10 0.5562E-01 -3.22 12 0.2932E-01 -3.51 14 0.1661E-01 -3.69 16 0.1000E-01 -3.80 18 0.6339E-02 -3.87 20 0.4195E-02 -3.92 TEST03 i tave(i) f at tave(i) bcoef(i) 1 0.00000 -162.00000 -162.00000 2 0.33333 -130.96296 -129.00000 3 1.00000 -80.00000 -75.00000 4 2.00000 -28.00000 -24.00000 5 3.00000 0.00000 3.00000 6 4.00000 10.00000 12.00000 7 5.00000 8.00000 9.00000 8 6.00000 0.00000 0.00000 9 7.00000 -8.00000 -9.00000 10 8.00000 -10.00000 -12.00000 11 9.00000 0.00000 -3.00000 12 9.66667 16.29630 15.00000 13 10.00000 28.00000 28.00000 TEST04 1 x b1(x) b2(x) b3(x) b4(x) b5(x) 0.000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.200 0.0400000 0.0000000 0.0000000 0.0000000 0.0000000 0.400 0.1600000 0.0000000 0.0000000 0.0000000 0.0000000 0.600 0.3600000 0.0000000 0.0000000 0.0000000 0.0000000 0.800 0.6400000 0.0000000 0.0000000 0.0000000 0.0000000 1.000 1.0000000 0.0000000 0.0000000 0.0000000 0.0000000 1.200 0.8100000 0.1833333 0.0066667 0.0000000 0.0000000 1.400 0.6400000 0.3333333 0.0266667 0.0000000 0.0000000 1.600 0.4900000 0.4500000 0.0600000 0.0000000 0.0000000 1.800 0.3600000 0.5333333 0.1066667 0.0000000 0.0000000 2.000 0.2500000 0.5833333 0.1666667 0.0000000 0.0000000 2.200 0.1600000 0.6000000 0.2400000 0.0000000 0.0000000 2.400 0.0900000 0.5833333 0.3266667 0.0000000 0.0000000 2.600 0.0400000 0.5333333 0.4266667 0.0000000 0.0000000 2.800 0.0100000 0.4500000 0.5400000 0.0000000 0.0000000 3.000 0.0000000 0.3333333 0.6666667 0.0000000 0.0000000 3.200 0.0000000 0.2133333 0.7733333 0.0133333 0.0000000 3.400 0.0000000 0.1200000 0.8266667 0.0533333 0.0000000 3.600 0.0000000 0.0533333 0.8266667 0.1200000 0.0000000 3.800 0.0000000 0.0133333 0.7733333 0.2133333 0.0000000 4.000 0.0000000 0.0000000 0.6666667 0.3333333 0.0000000 4.200 0.0000000 0.0000000 0.5400000 0.4500000 0.0100000 4.400 0.0000000 0.0000000 0.4266667 0.5333333 0.0400000 4.600 0.0000000 0.0000000 0.3266667 0.5833333 0.0900000 4.800 0.0000000 0.0000000 0.2400000 0.6000000 0.1600000 5.000 0.0000000 0.0000000 0.1666667 0.5833333 0.2500000 5.200 0.0000000 0.0000000 0.1066667 0.5333333 0.3600000 5.400 0.0000000 0.0000000 0.0600000 0.4500000 0.4900000 5.600 0.0000000 0.0000000 0.0266667 0.3333333 0.6400000 5.800 0.0000000 0.0000000 0.0066667 0.1833333 0.8100000 6.000 0.0000000 0.0000000 0.0000000 0.0000000 1.0000000 TEST05 -0.8 -0.04266667 1.12373333 -17.16693333 10.48106667 -0.6 -0.01800000 0.80120000 -14.75080000 9.58320000 -0.4 -0.00533333 0.54346667 -12.55786667 8.73813333 -0.2 -0.00066667 0.34493333 -10.57773333 7.94426667 0.0 0.00000000 0.20000000 -8.80000000 7.20000000 0.2 0.00066667 0.10306667 -7.21426667 6.50373333 0.4 0.00533333 0.04853333 -5.81013333 5.85386667 0.6 0.01800000 0.03080000 -4.57720000 5.24880000 0.8 0.04266667 0.04426667 -3.50506667 4.68693333 1.0 0.08333333 0.08333333 -2.58333333 4.16666667 1.2 0.14400000 0.14240000 -1.80160000 3.68640000 1.4 0.22866667 0.21586667 -1.14946667 3.24453333 1.6 0.34133333 0.29813333 -0.61653333 2.83946667 1.8 0.48600000 0.38360000 -0.19240000 2.46960000 2.0 0.66666667 0.46666667 0.13333333 2.13333333 2.2 0.88733333 0.54173333 0.37106667 1.82906667 2.4 1.15200000 0.60320000 0.53120000 1.55520000 2.6 1.46466667 0.64546667 0.62413333 1.31013333 2.8 1.82933333 0.66293333 0.66026667 1.09226667 3.0 2.25000000 0.65000000 0.65000000 0.90000000 3.2 2.73066667 0.60106667 0.60373333 0.73173333 3.4 3.27533333 0.51053333 0.53186667 0.58586667 3.6 3.88800000 0.37280000 0.44480000 0.46080000 3.8 4.57266667 0.18226667 0.35293333 0.35493333 4.0 5.33333333 -0.06666667 0.26666667 0.26666667 4.2 6.17400000 -0.37960000 0.19640000 0.19440000 4.4 7.09866667 -0.76213333 0.15253333 0.13653333 4.6 8.11133333 -1.21986667 0.14546667 0.09146667 4.8 9.21600000 -1.75840000 0.18560000 0.05760000 5.0 10.41666667 -2.38333333 0.28333333 0.03333333 5.2 11.71733333 -3.10026667 0.44906667 0.01706667 5.4 13.12200000 -3.91480000 0.69320000 0.00720000 5.6 14.63466667 -4.83253333 1.02613333 0.00213333 5.8 16.25933333 -5.85906667 1.45826667 0.00026667 6.0 18.00000000 -7.00000000 2.00000000 0.00000000 6.2 19.86066667 -8.26093333 2.66173333 -0.00026667 6.4 21.84533333 -9.64746667 3.45386667 -0.00213333 6.6 23.95800000 -11.16520000 4.38680000 -0.00720000 6.8 26.20266667 -12.81973333 5.47093333 -0.01706667 7.0 28.58333333 -14.61666667 6.71666667 -0.03333333 TEST06 -0.8 -0.04266667 -0.6 -0.01800000 -0.4 -0.00533333 -0.2 -0.00066667 0.0 0.00000000 0.2 0.00066667 0.4 0.00533333 0.6 0.01800000 0.8 0.04266667 1.0 0.08333333 1.2 0.14240000 1.4 0.21586667 1.6 0.29813333 1.8 0.38360000 2.0 0.46666667 2.2 0.54173333 2.4 0.60320000 2.6 0.64546667 2.8 0.66293333 3.0 0.65000000 3.2 0.60373333 3.4 0.53186667 3.6 0.44480000 3.8 0.35293333 4.0 0.26666667 4.2 0.19440000 4.4 0.13653333 4.6 0.09146667 4.8 0.05760000 5.0 0.03333333 5.2 0.01706667 5.4 0.00720000 5.6 0.00213333 5.8 0.00026667 6.0 0.00000000 6.2 -0.00026667 6.4 -0.00213333 6.6 -0.00720000 6.8 -0.01706667 7.0 -0.03333333 TEST07 -0.8 0.00000000 -0.6 0.00000000 -0.4 0.00000000 -0.2 0.00000000 0.0 0.00000000 0.2 0.00066667 0.4 0.00533333 0.6 0.01800000 0.8 0.04266667 1.0 0.08333334 1.2 0.14240001 1.4 0.21586668 1.6 0.29813335 1.8 0.38360002 2.0 0.46666668 2.2 0.54173335 2.4 0.60320001 2.6 0.64546667 2.8 0.66293333 3.0 0.64999999 3.2 0.60373331 3.4 0.53186664 3.6 0.44479997 3.8 0.35293330 4.0 0.26666664 4.2 0.19439997 4.4 0.13653331 4.6 0.09146665 4.8 0.05759999 5.0 0.03333332 5.2 0.01706666 5.4 0.00720000 5.6 0.00213333 5.8 0.00026667 6.0 0.00000000 6.2 0.00000000 6.4 0.00000000 6.6 0.00000000 6.8 0.00000000 7.0 0.00000000 TEST08 n max.error decay exp. 4 0.3834E+03 0.00 6 0.1285E+03 -2.70 8 0.4653E+02 -3.53 10 0.1316E+02 -5.66 n max.error decay exp. 4 0.4882E+02 0.00 6 0.1179E+02 -3.50 8 0.2897E+01 -4.88 10 0.5740E+00 -7.25 12 0.1384E+00 -7.80 14 0.8384E-01 -3.25 16 0.5457E-01 -3.21 18 0.3749E-01 -3.19 20 0.2685E-01 -3.17 n max.error decay exp. 4 0.5001E+01 0.00 6 0.7842E+00 -4.57 8 0.1217E+00 -6.48 10 0.5025E-01 -3.96 12 0.3364E-01 -2.20 14 0.2408E-01 -2.17 16 0.1809E-01 -2.14 18 0.1408E-01 -2.13 20 0.1127E-01 -2.11 TEST09 0 cycles through newnot n max.error decay exp. 4 0.1476E+00 0.00 6 0.1114E+00 -0.69 8 0.9414E-01 -0.59 10 0.8303E-01 -0.56 12 0.7510E-01 -0.55 14 0.6908E-01 -0.54 16 0.6431E-01 -0.54 18 0.6041E-01 -0.53 20 0.5714E-01 -0.53 3 cycles through newnot n max.error decay exp. 4 0.1539E+00 0.00 6 0.1293E+00 -0.43 8 0.1098E+00 -0.57 10 0.9437E-01 -0.68 12 0.8363E-01 -0.66 14 0.7535E-01 -0.68 16 0.6880E-01 -0.68 18 0.6348E-01 -0.68 20 0.5911E-01 -0.68 TEST10 n max.error decay exp. 4 0.7240E+00 0.00 6 0.9952E-01 -4.89 8 0.3031E-01 -4.13 10 0.1197E-01 -4.17 n max.error decay exp. 4 0.4128E+00 0.00 6 0.8937E-01 -3.77 8 0.3257E-01 -3.51 10 0.1532E-01 -3.38 12 0.8393E-02 -3.30 14 0.5085E-02 -3.25 16 0.3310E-02 -3.21 18 0.2274E-02 -3.19 20 0.1629E-02 -3.17 TEST11 size of noise =0.10E-05 h max.error 0.17E+00 0.145E-05 0.83E-01 0.251E-05 0.42E-01 0.676E-05 0.21E-01 0.158E-04 0.10E-01 0.342E-04 0.52E-02 0.712E-04 0.26E-02 0.145E-03 0.13E-02 0.294E-03 0.65E-03 0.591E-03 0.33E-03 0.119E-02 size of noise =0.00E+00 h max.error 0.17E+00 0.133E-14 0.83E-01 0.888E-15 0.42E-01 0.133E-14 0.21E-01 0.266E-14 0.10E-01 0.488E-14 0.52E-02 0.377E-14 0.26E-02 0.266E-13 0.13E-02 0.444E-13 0.65E-03 0.113E-12 0.33E-03 0.879E-13 TEST12 0 cycles through newnot n max.error decay exp. 4 0.1476E+00 0.00 6 0.9126E-01 -1.19 8 0.7070E-01 -0.89 10 0.5975E-01 -0.75 12 0.5270E-01 -0.69 14 0.4767E-01 -0.65 16 0.4385E-01 -0.63 18 0.4082E-01 -0.61 20 0.3834E-01 -0.59 3 cycles through newnot n max.error decay exp. 4 0.1476E+00 0.00 6 0.7753E-01 -1.59 8 0.4044E-01 -2.26 10 0.2593E-01 -1.99 12 0.1822E-01 -1.94 14 0.1364E-01 -1.88 16 0.1065E-01 -1.85 18 0.8637E-02 -1.78 20 0.7159E-02 -1.78 6 cycles through newnot n max.error decay exp. 4 0.1476E+00 0.00 6 0.7545E-01 -1.65 8 0.3413E-01 -2.76 10 0.1870E-01 -2.70 12 0.1139E-01 -2.72 14 0.7548E-02 -2.67 16 0.5330E-02 -2.61 18 0.3926E-02 -2.60 20 0.3009E-02 -2.52 TEST13 0 cycles through newnot n max.error decay exp. 4 0.1476E+00 0.00 6 0.9126E-01 -1.19 8 0.6436E-01 -1.21 10 0.4382E-01 -1.72 12 0.2896E-01 -2.27 14 0.1919E-01 -2.67 16 0.1278E-01 -3.04 18 0.8604E-02 -3.36 20 0.5865E-02 -3.64 1 cycles through newnot n max.error decay exp. 4 0.1476E+00 0.00 6 0.8335E-01 -1.41 8 0.5004E-01 -1.77 10 0.2833E-01 -2.55 12 0.1647E-01 -2.97 14 0.9871E-02 -3.32 16 0.6104E-02 -3.60 18 0.3895E-02 -3.81 20 0.2567E-02 -3.96 2 cycles through newnot n max.error decay exp. 4 0.1476E+00 0.00 6 0.7954E-01 -1.52 8 0.4188E-01 -2.23 10 0.2240E-01 -2.81 12 0.1259E-01 -3.16 14 0.7394E-02 -3.45 16 0.4526E-02 -3.68 18 0.2877E-02 -3.85 20 0.1891E-02 -3.98 TEST14 i, data point, data, interpolant, error 1 595. 0.6440 0.6440 0.000E+00 2 605. 0.6220 0.1043 0.518E+00 3 615. 0.6380 0.0436 0.594E+00 4 625. 0.6490 0.2781 0.371E+00 5 635. 0.6520 0.6520 0.111E-15 6 645. 0.6390 1.0378 -0.399E+00 7 655. 0.6460 1.3359 -0.690E+00 8 665. 0.6570 1.4749 -0.818E+00 9 675. 0.6520 1.4114 -0.759E+00 10 685. 0.6550 1.1302 -0.475E+00 11 695. 0.6440 0.6440 0.111E-15 12 705. 0.6630 -0.0062 0.669E+00 13 715. 0.6630 -0.7513 0.141E+01 14 725. 0.6680 -1.4943 0.216E+01 15 735. 0.6760 -2.1102 0.279E+01 16 745. 0.6760 -2.4607 0.314E+01 17 755. 0.6860 -2.4516 0.314E+01 18 765. 0.6790 -2.0563 0.274E+01 19 775. 0.6780 -1.3160 0.199E+01 20 785. 0.6830 -0.3401 0.102E+01 21 795. 0.6940 0.6940 0.000E+00 22 805. 0.6990 1.5515 -0.853E+00 23 815. 0.7100 2.0381 -0.133E+01 24 825. 0.7300 2.0863 -0.136E+01 25 835. 0.7630 1.7620 -0.999E+00 26 845. 0.8120 1.2646 -0.453E+00 27 855. 0.9070 0.9070 -0.111E-15 28 865. 1.0440 0.9300 0.114E+00 29 875. 1.3360 1.3360 -0.222E-15 30 885. 1.8810 1.8775 0.354E-02 31 895. 2.1690 2.1690 0.444E-15 32 905. 2.0750 2.0308 0.442E-01 33 915. 1.5980 1.5980 -0.222E-15 34 925. 1.2110 1.1682 0.428E-01 35 935. 0.9160 0.9160 -0.222E-15 36 945. 0.7460 0.8395 -0.935E-01 37 955. 0.6720 0.8294 -0.157E+00 38 965. 0.6270 0.8007 -0.174E+00 39 975. 0.6150 0.7207 -0.106E+00 40 985. 0.6070 0.6070 0.222E-15 41 995. 0.6060 0.5031 0.103E+00 42 1005. 0.6090 0.4419 0.167E+00 43 1015. 0.6030 0.4403 0.163E+00 44 1025. 0.6010 0.4990 0.102E+00 45 1035. 0.6030 0.6030 -0.111E-15 46 1045. 0.6010 0.7211 -0.120E+00 47 1055. 0.6110 0.8060 -0.195E+00 48 1065. 0.6010 0.7947 -0.194E+00 49 1075. 0.6080 0.6080 0.000E+00 optimal knots = 1 730.985426501 2 794.413722071 3 844.476450939 4 880.059523937 5 907.814105444 6 938.000512684 7 976.751678736 TEST15 exact values rounded to 2 digits after decimal point. value and derivatives of noisefree function at some points 1 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.5000000E+00 6 0.1041667E-01 0.6250000E-01 0.2500000E+00 0.5000000E+00 11 0.8333333E-01 0.2500000E+00 0.5000000E+00 -0.7000000E+00 16 0.2562500E+00 0.4125000E+00 0.1500000E+00 -0.7000000E+00 21 0.4666667E+00 0.4000000E+00 -0.2000000E+00 -0.7000000E+00 26 0.6270833E+00 0.2125000E+00 -0.5500000E+00 -0.7000000E+00 31 0.6500000E+00 -0.1500000E+00 -0.9000000E+00 0.1300000E+01 36 0.4895833E+00 -0.4375000E+00 -0.2500000E+00 0.1300000E+01 41 0.2666667E+00 -0.4000000E+00 0.4000000E+00 -0.2000000E+00 46 0.1125000E+00 -0.2250000E+00 0.3000000E+00 -0.2000000E+00 51 0.3333333E-01 -0.1000000E+00 0.2000000E+00 -0.2000000E+00 56 0.4166667E-02 -0.2500000E-01 0.1000000E+00 -0.2000000E+00 61 0.5551115E-16 0.0000000E+00 0.0000000E+00 -0.2000000E+00 prescribed s = 0.600E+06, s(smoothing spline) = 0.137E+06 value and derivatives of smoothing spline at corresp. points 1 0.2941036E+00 -0.1617663E-01 0.0000000E+00 0.0000000E+00 6 0.2860153E+00 -0.1617663E-01 0.0000000E+00 0.0000000E+00 11 0.2779270E+00 -0.1617663E-01 0.0000000E+00 0.0000000E+00 16 0.2698387E+00 -0.1617663E-01 0.0000000E+00 0.0000000E+00 21 0.2617504E+00 -0.1617663E-01 0.0000000E+00 0.0000000E+00 26 0.2536621E+00 -0.1617663E-01 0.0000000E+00 0.0000000E+00 31 0.2455738E+00 -0.1617663E-01 0.0000000E+00 0.0000000E+00 36 0.2374855E+00 -0.1617663E-01 0.0000000E+00 0.0000000E+00 41 0.2293971E+00 -0.1617663E-01 0.0000000E+00 0.0000000E+00 46 0.2213088E+00 -0.1617663E-01 0.0000000E+00 0.0000000E+00 51 0.2132205E+00 -0.1617663E-01 0.0000000E+00 0.0000000E+00 56 0.2051322E+00 -0.1617663E-01 0.0000000E+00 0.0000000E+00 61 0.1970439E+00 -0.1617663E-01 0.0000000E+00 0.0000000E+00 prescribed s = 0.600E+05, s(smoothing spline) = 0.606E+05 value and derivatives of smoothing spline at corresp. points 1 0.1147453E+00 0.1248896E+00 0.0000000E+00 -0.3144359E-02 6 0.1770639E+00 0.1239407E+00 -0.5373302E-02 -0.2344597E-01 11 0.2377963E+00 0.1176221E+00 -0.2177277E-01 -0.4643046E-01 16 0.2928591E+00 0.1004183E+00 -0.4818482E-01 -0.5869598E-01 21 0.3358277E+00 0.6906420E-01 -0.7672704E-01 -0.4991272E-01 26 0.3598108E+00 0.2521816E-01 -0.9641122E-01 -0.2004025E-01 31 0.3600840E+00 -0.2429080E-01 -0.9838592E-01 0.2024727E-01 36 0.3361813E+00 -0.6990344E-01 -0.8151629E-01 0.4990104E-01 41 0.2921234E+00 -0.1040603E+00 -0.5446361E-01 0.5577702E-01 46 0.2344183E+00 -0.1246005E+00 -0.2863262E-01 0.4312783E-01 51 0.1693762E+00 -0.1340802E+00 -0.1079232E-01 0.2425146E-01 56 0.1014326E+00 -0.1369733E+00 -0.2101441E-02 0.8258699E-02 61 0.3281814E-01 -0.1373147E+00 0.0000000E+00 0.8993137E-03 prescribed s = 0.600E+04, s(smoothing spline) = 0.601E+04 value and derivatives of smoothing spline at corresp. points 1 -0.7700496E-01 0.2016251E+00 0.0000000E+00 0.8348940E-01 6 0.2640664E-01 0.2191499E+00 0.8231865E-01 0.1899203E+00 11 0.1495967E+00 0.2779315E+00 0.1320411E+00 -0.9156231E-01 16 0.3019495E+00 0.3217662E+00 0.1666312E-01 -0.4016292E+00 21 0.4560014E+00 0.2752966E+00 -0.2109408E+00 -0.4678783E+00 26 0.5580908E+00 0.1166162E+00 -0.4065841E+00 -0.2165549E+00 31 0.5625813E+00 -0.1000095E+00 -0.4224959E+00 0.2521956E+00 36 0.4663443E+00 -0.2682390E+00 -0.2245256E+00 0.5361252E+00 41 0.3152549E+00 -0.3146008E+00 0.3119113E-01 0.4085792E+00 46 0.1693283E+00 -0.2574074E+00 0.1714570E+00 0.8681967E-01 51 0.6291959E-01 -0.1691475E+00 0.1614270E+00 -0.1512137E+00 56 -0.5006900E-02 -0.1104196E+00 0.6876211E-01 -0.1935220E+00 61 -0.5528434E-01 -0.9657137E-01 0.0000000E+00 -0.5993972E-01 prescribed s = 0.600E+03, s(smoothing spline) = 0.601E+03 value and derivatives of smoothing spline at corresp. points 1 -0.2963400E-01 0.7784390E-01 0.0000000E+00 0.1881186E+00 6 0.1512881E-01 0.1172257E+00 0.1860182E+00 0.4513100E+00 11 0.1052990E+00 0.2556813E+00 0.3274437E+00 -0.1074509E+00 16 0.2695089E+00 0.3856242E+00 0.1453313E+00 -0.6319346E+00 21 0.4664125E+00 0.3713366E+00 -0.2193693E+00 -0.7647145E+00 26 0.6094399E+00 0.1723324E+00 -0.5596879E+00 -0.4544145E+00 31 0.6189989E+00 -0.1388067E+00 -0.6152950E+00 0.4415859E+00 36 0.4845194E+00 -0.3686379E+00 -0.2554097E+00 0.9618103E+00 41 0.2875115E+00 -0.3840732E+00 0.1638807E+00 0.5533942E+00 46 0.1252297E+00 -0.2533486E+00 0.3071757E+00 -0.4324249E-01 51 0.3494297E-01 -0.1145944E+00 0.2279962E+00 -0.2802139E+00 56 0.1160666E-03 -0.3662131E-01 0.8773735E-01 -0.2464744E+00 61 -0.1190576E-01 -0.1897948E-01 -0.8673617E-18 -0.7557853E-01 prescribed s = 0.600E+02, s(smoothing spline) = 0.600E+02 value and derivatives of smoothing spline at corresp. points 1 -0.8394129E-02 0.2581047E-01 0.0000000E+00 0.2518230E+00 6 0.1198464E-01 0.7524758E-01 0.2300879E+00 0.5644270E+00 11 0.8923731E-01 0.2504282E+00 0.4184971E+00 -0.2174806E+00 16 0.2591358E+00 0.4062645E+00 0.1575786E+00 -0.6429156E+00 21 0.4678743E+00 0.3973185E+00 -0.2160043E+00 -0.7442283E+00 26 0.6247285E+00 0.1993882E+00 -0.5940418E+00 -0.7224763E+00 31 0.6391664E+00 -0.1522376E+00 -0.7223112E+00 0.5305745E+00 36 0.4878095E+00 -0.4132885E+00 -0.2530386E+00 0.1289184E+01 41 0.2740688E+00 -0.3996796E+00 0.2468044E+00 0.5556576E+00 46 0.1133045E+00 -0.2373620E+00 0.3303067E+00 -0.1861492E+00 51 0.3150310E-01 -0.9930279E-01 0.2192157E+00 -0.2914548E+00 56 0.2946336E-02 -0.2602364E-01 0.9223091E-01 -0.2136055E+00 61 -0.3058048E-02 -0.6123582E-02 0.0000000E+00 -0.9174112E-01 prescribed s = 0.600E+01, s(smoothing spline) = 0.602E+01 value and derivatives of smoothing spline at corresp. points 1 -0.7761942E-04 -0.3258983E-02 0.0000000E+00 0.2902726E+00 6 0.1196397E-01 0.5910886E-01 0.3700503E+00 -0.1852071E+01 11 0.8113751E-01 0.2499691E+00 0.6298765E+00 -0.2068756E+01 16 0.2597290E+00 0.4002764E+00 -0.4646067E-01 0.7199026E+00 21 0.4704100E+00 0.4034641E+00 -0.4440256E+00 -0.1965103E+01 26 0.6287927E+00 0.2457430E+00 -0.8246287E+00 -0.2005511E+01 31 0.6490559E+00 -0.1504916E+00 -0.9944092E+00 0.1616665E+01 36 0.4882313E+00 -0.4450990E+00 -0.4212975E+00 0.6255360E+01 41 0.2690242E+00 -0.4038389E+00 0.1370717E-01 0.2163886E+01 46 0.1116081E+00 -0.2373397E+00 0.3946836E+00 -0.3037040E+00 51 0.2979722E-01 -0.9931821E-01 0.3889785E+00 0.4965903E+00 56 0.2233020E-02 -0.4057103E-01 0.4159226E+00 -0.2142740E+01 61 0.2673157E-04 0.1638648E-03 0.0000000E+00 0.9996781E-01 prescribed s = 0.600E+00, s(smoothing spline) = 0.602E+00 value and derivatives of smoothing spline at corresp. points 1 -0.1199480E-05 0.1596481E-03 0.0000000E+00 0.9792433E-01 6 0.1066315E-01 0.3943016E-01 0.1660023E+01 -0.1882883E+02 11 0.8046364E-01 0.2499976E+00 0.1445672E+01 -0.1892289E+02 16 0.2599986E+00 0.4000181E+00 0.4376973E-02 0.4982062E-01 21 0.4704912E+00 0.3992611E+00 0.4603068E+00 -0.1891737E+02 26 0.6297978E+00 0.2591464E+00 -0.1208571E+01 0.2336277E+01 31 0.6500599E+00 -0.1500205E+00 -0.9768544E+00 -0.2434928E+01 36 0.4893052E+00 -0.4598538E+00 -0.1667521E+01 0.3547889E+02 41 0.2700603E+00 -0.3998548E+00 0.2365105E-01 -0.2360405E+01 46 0.1106938E+00 -0.2600053E+00 0.1669383E+01 -0.2138201E+02 51 0.2947728E-01 -0.9997954E-01 -0.4677549E+00 0.2132809E+02 56 0.6645464E-03 -0.6055177E-01 0.1655647E+01 -0.1889271E+02 61 0.6698039E-07 -0.4084469E-05 0.0000000E+00 0.5468210E-02 TEST16 carrier,s nonlinear perturb. problem eps 0.5000000000E-02 approximation from a space of splines of order 6 on 4 intervals, of dimension 18. breakpoints - 0.2500000000E+00 0.5000000000E+00 0.7500000000E+00 after 5 of 10 allowed iterations, the pp representation of the approximation is 0.000-0.100000E+01 0.222E-14 -0.200E-05 0.305E-03 -0.873E-02 0.132E+00 0.250-0.100000E+01 0.769E-05 -0.436E-03 0.467E-01 -0.130E+01 0.193E+02 0.500-0.999944E+00 0.112E-02 -0.629E-01 0.676E+01 -0.188E+03 0.280E+04 0.750-0.991799E+00 0.163E+00 0.452E+01 -0.139E+02 0.215E+04 0.609E+05 x, g(x) and g(x)-f(x) at selected points 0.7500000000E+00 -0.9918430577E+00 -0.4371193014E-04 0.7812500000E+00 -0.9847788097E+00 -0.3273764484E-03 0.8125000000E+00 -0.9716256847E+00 -0.1661461272E-03 0.8437500000E+00 -0.9472073045E+00 0.6934479058E-03 0.8750000000E+00 -0.9021227536E+00 0.1047737394E-02 0.9062500000E+00 -0.8197249364E+00 -0.5564475749E-03 0.9375000000E+00 -0.6719498792E+00 -0.3465088124E-02 0.9687500000E+00 -0.4159958955E+00 -0.3410149036E-02 0.1000000000E+01 -0.1110223025E-15 -0.1110223025E-15 approximation from a space of splines of order 6 on 4 intervals, of dimension 18. breakpoints - 0.4414279015E+00 0.6527660437E+00 0.8313478654E+00 after 2 of 10 allowed iterations, the pp representation of the approximation is 0.000-0.100000E+01 -0.126E-14 -0.343E-03 0.138E-01 -0.227E+00 0.151E+01 0.441-0.999983E+00 0.338E-03 -0.208E-02 0.936E+00 -0.273E+02 0.548E+03 0.653-0.998831E+00 0.234E-01 0.260E+00 0.315E+02 -0.819E+03 0.242E+05 0.831-0.958712E+00 0.820E+00 0.199E+02 -0.971E+02 0.235E+05 -0.155E+06 x, g(x) and g(x)-f(x) at selected points 0.7500000000E+00 -0.9918430577E+00 -0.3836478288E-04 0.7812500000E+00 -0.9847788097E+00 0.1502825292E-04 0.8125000000E+00 -0.9716256847E+00 0.1881754721E-04 0.8437500000E+00 -0.9472073045E+00 -0.1881834588E-03 0.8750000000E+00 -0.9021227536E+00 -0.1826311487E-03 0.9062500000E+00 -0.8197249364E+00 0.7550064203E-03 0.9375000000E+00 -0.6719498792E+00 0.9169966546E-04 0.9687500000E+00 -0.4159958955E+00 -0.1261968911E-02 0.1000000000E+01 -0.1110223025E-15 0.0000000000E+00 approximation from a space of splines of order 6 on 4 intervals, of dimension 18. breakpoints - 0.4450307232E+00 0.6788946009E+00 0.8464961162E+00 after 1 of 10 allowed iterations, the pp representation of the approximation is 0.000-0.100000E+01 0.000E+00 -0.373E-03 0.149E-01 -0.242E+00 0.160E+01 0.445-0.999981E+00 0.365E-03 -0.109E-01 0.161E+01 -0.461E+02 0.769E+03 0.679-0.998028E+00 0.394E-01 0.554E+00 0.424E+02 -0.989E+03 0.351E+05 0.846-0.944246E+00 0.110E+01 0.253E+02 -0.250E+02 0.290E+05 -0.254E+06 x, g(x) and g(x)-f(x) at selected points 0.7500000000E+00 -0.9918430577E+00 -0.3355605289E-04 0.7812500000E+00 -0.9847788097E+00 -0.2214734181E-04 0.8125000000E+00 -0.9716256847E+00 0.3123607127E-04 0.8437500000E+00 -0.9472073045E+00 -0.7021378316E-05 0.8750000000E+00 -0.9021227536E+00 -0.3033227785E-03 0.9062500000E+00 -0.8197249364E+00 0.4146220564E-03 0.9375000000E+00 -0.6719498792E+00 0.3326326211E-03 0.9687500000E+00 -0.4159958955E+00 -0.8404834847E-03 0.1000000000E+01 -0.1110223025E-15 -0.1110223025E-15 TEST17 gamma = ? (f10.3) cubic spline vs. taut spline with gamma = 2.500 595.0000000 0.64400000E+00 0.64400000E+00 597.4000000 0.64536674E+00 0.64520641E+00 599.8000000 0.64659330E+00 0.64630048E+00 602.2000000 0.64768520E+00 0.64728624E+00 604.6000000 0.64864795E+00 0.64816769E+00 607.0000000 0.64948709E+00 0.64894883E+00 609.4000000 0.65020812E+00 0.64963368E+00 611.8000000 0.65081656E+00 0.65022624E+00 614.2000000 0.65131793E+00 0.65073052E+00 616.6000000 0.65171775E+00 0.65115053E+00 619.0000000 0.65202154E+00 0.65149027E+00 621.4000000 0.65223481E+00 0.65175377E+00 623.8000000 0.65236309E+00 0.65194501E+00 626.2000000 0.65241189E+00 0.65206802E+00 628.6000000 0.65238672E+00 0.65212679E+00 631.0000000 0.65229312E+00 0.65212535E+00 633.4000000 0.65213659E+00 0.65206769E+00 635.8000000 0.65192265E+00 0.65195783E+00 638.2000000 0.65165682E+00 0.65179976E+00 640.6000000 0.65134463E+00 0.65159751E+00 643.0000000 0.65099158E+00 0.65135508E+00 645.4000000 0.65060319E+00 0.65107647E+00 647.8000000 0.65018499E+00 0.65076570E+00 650.2000000 0.64974249E+00 0.65042677E+00 652.6000000 0.64928122E+00 0.65006369E+00 655.0000000 0.64880668E+00 0.64968047E+00 657.4000000 0.64832439E+00 0.64928112E+00 659.8000000 0.64783988E+00 0.64886964E+00 662.2000000 0.64735866E+00 0.64845005E+00 664.6000000 0.64688625E+00 0.64802635E+00 667.0000000 0.64642817E+00 0.64760255E+00 669.4000000 0.64598994E+00 0.64718266E+00 671.8000000 0.64557707E+00 0.64677069E+00 674.2000000 0.64519508E+00 0.64637064E+00 676.6000000 0.64484949E+00 0.64598652E+00 679.0000000 0.64454582E+00 0.64562234E+00 681.4000000 0.64428959E+00 0.64528211E+00 683.8000000 0.64408631E+00 0.64496984E+00 686.2000000 0.64394151E+00 0.64468953E+00 688.6000000 0.64386070E+00 0.64444520E+00 691.0000000 0.64384939E+00 0.64424085E+00 693.4000000 0.64391311E+00 0.64408049E+00 695.8000000 0.64405733E+00 0.64396810E+00 698.2000000 0.64428456E+00 0.64390594E+00 700.6000000 0.64459272E+00 0.64389365E+00 703.0000000 0.64497936E+00 0.64393060E+00 705.4000000 0.64544202E+00 0.64401619E+00 707.8000000 0.64597823E+00 0.64414981E+00 710.2000000 0.64658552E+00 0.64433084E+00 712.6000000 0.64726144E+00 0.64455869E+00 715.0000000 0.64800353E+00 0.64483274E+00 717.4000000 0.64880931E+00 0.64515238E+00 719.8000000 0.64967633E+00 0.64551700E+00 722.2000000 0.65060212E+00 0.64592599E+00 724.6000000 0.65158422E+00 0.64637874E+00 727.0000000 0.65262017E+00 0.64687465E+00 729.4000000 0.65370750E+00 0.64741310E+00 731.8000000 0.65484376E+00 0.64799348E+00 734.2000000 0.65602647E+00 0.64861518E+00 736.6000000 0.65725318E+00 0.64927761E+00 739.0000000 0.65852142E+00 0.64998013E+00 741.4000000 0.65982873E+00 0.65072215E+00 743.8000000 0.66117265E+00 0.65150306E+00 746.2000000 0.66255071E+00 0.65232224E+00 748.6000000 0.66396045E+00 0.65317910E+00 751.0000000 0.66539941E+00 0.65407300E+00 753.4000000 0.66686513E+00 0.65500396E+00 755.8000000 0.66835514E+00 0.65598166E+00 758.2000000 0.66986697E+00 0.65702375E+00 760.6000000 0.67139818E+00 0.65814812E+00 763.0000000 0.67294628E+00 0.65937263E+00 765.4000000 0.67450883E+00 0.66071517E+00 767.8000000 0.67608335E+00 0.66219360E+00 770.2000000 0.67766739E+00 0.66382582E+00 772.6000000 0.67925848E+00 0.66562969E+00 775.0000000 0.68085416E+00 0.66762309E+00 777.4000000 0.68245196E+00 0.66982390E+00 779.8000000 0.68404943E+00 0.67224999E+00 782.2000000 0.68564409E+00 0.67491925E+00 784.6000000 0.68723349E+00 0.67784954E+00 787.0000000 0.68881517E+00 0.68105874E+00 789.4000000 0.69038666E+00 0.68456474E+00 791.8000000 0.69194549E+00 0.68838540E+00 794.2000000 0.69348921E+00 0.69253861E+00 796.6000000 0.69501890E+00 0.69704079E+00 799.0000000 0.69657684E+00 0.70189152E+00 801.4000000 0.69823191E+00 0.70707951E+00 803.8000000 0.70005344E+00 0.71259330E+00 806.2000000 0.70211073E+00 0.71842140E+00 808.6000000 0.70447311E+00 0.72455236E+00 811.0000000 0.70720989E+00 0.73097469E+00 813.4000000 0.71039039E+00 0.73767694E+00 815.8000000 0.71408393E+00 0.74464762E+00 818.2000000 0.71835983E+00 0.75187527E+00 820.6000000 0.72328741E+00 0.75934841E+00 823.0000000 0.72893599E+00 0.76705559E+00 825.4000000 0.73537487E+00 0.77498532E+00 827.8000000 0.74267339E+00 0.78312613E+00 830.2000000 0.75090086E+00 0.79146656E+00 832.6000000 0.76012659E+00 0.79999513E+00 835.0000000 0.77041991E+00 0.80871255E+00 837.4000000 0.78185013E+00 0.81772006E+00 839.8000000 0.79448658E+00 0.82716850E+00 842.2000000 0.80839856E+00 0.83720904E+00 844.6000000 0.82365541E+00 0.84799288E+00 847.0000000 0.84032643E+00 0.85967118E+00 849.4000000 0.85848094E+00 0.87239514E+00 851.8000000 0.87818827E+00 0.88631592E+00 854.2000000 0.89951773E+00 0.90158471E+00 856.6000000 0.92262739E+00 0.91846693E+00 859.0000000 0.94870714E+00 0.93855588E+00 861.4000000 0.97961252E+00 0.96430159E+00 863.8000000 0.10172102E+01 0.99816837E+00 866.2000000 0.10633668E+01 0.10426205E+01 868.6000000 0.11199490E+01 0.11001224E+01 871.0000000 0.11888234E+01 0.11731382E+01 873.4000000 0.12718566E+01 0.12641324E+01 875.8000000 0.13708645E+01 0.13754968E+01 878.2000000 0.14846089E+01 0.15052854E+01 880.6000000 0.16071177E+01 0.16448282E+01 883.0000000 0.17320121E+01 0.17848764E+01 885.4000000 0.18529130E+01 0.19161815E+01 887.8000000 0.19634412E+01 0.20294950E+01 890.2000000 0.20572178E+01 0.21155683E+01 892.6000000 0.21278638E+01 0.21651528E+01 895.0000000 0.21690000E+01 0.21690000E+01 897.4000000 0.21761280E+01 0.21252777E+01 899.8000000 0.21522714E+01 0.20611871E+01 902.2000000 0.21023344E+01 0.19948271E+01 904.6000000 0.20312212E+01 0.19265998E+01 907.0000000 0.19438361E+01 0.18560391E+01 909.4000000 0.18450832E+01 0.17826790E+01 911.8000000 0.17398667E+01 0.17060532E+01 914.2000000 0.16330908E+01 0.16256957E+01 916.6000000 0.15294259E+01 0.15412491E+01 919.0000000 0.14308234E+01 0.14536207E+01 921.4000000 0.13374805E+01 0.13645339E+01 923.8000000 0.12495653E+01 0.12757255E+01 926.2000000 0.11672460E+01 0.11889322E+01 928.6000000 0.10906906E+01 0.11058910E+01 931.0000000 0.10200671E+01 0.10283388E+01 933.4000000 0.95554371E+00 0.95801230E+00 935.8000000 0.89728530E+00 0.89663153E+00 938.2000000 0.84527128E+00 0.84490145E+00 940.6000000 0.79919338E+00 0.80195386E+00 943.0000000 0.75871857E+00 0.76678522E+00 945.4000000 0.72351381E+00 0.73839201E+00 947.8000000 0.69324609E+00 0.71577069E+00 950.2000000 0.66758236E+00 0.69791772E+00 952.6000000 0.64618960E+00 0.68382959E+00 955.0000000 0.62873479E+00 0.67250275E+00 957.4000000 0.61488489E+00 0.66293368E+00 959.8000000 0.60430687E+00 0.65428226E+00 962.2000000 0.59666770E+00 0.64637301E+00 964.6000000 0.59163436E+00 0.63919939E+00 967.0000000 0.58887382E+00 0.63275486E+00 969.4000000 0.58805304E+00 0.62703287E+00 971.8000000 0.58883900E+00 0.62202687E+00 974.2000000 0.59089867E+00 0.61773033E+00 976.6000000 0.59389902E+00 0.61413671E+00 979.0000000 0.59750702E+00 0.61123945E+00 981.4000000 0.60138965E+00 0.60903203E+00 983.8000000 0.60521387E+00 0.60750788E+00 986.2000000 0.60865421E+00 0.60665237E+00 988.6000000 0.61155919E+00 0.60626429E+00 991.0000000 0.61395129E+00 0.60599062E+00 993.4000000 0.61586054E+00 0.60572156E+00 995.8000000 0.61731700E+00 0.60545788E+00 998.2000000 0.61835071E+00 0.60520084E+00 1000.6000000 0.61899171E+00 0.60495169E+00 1003.0000000 0.61927004E+00 0.60471170E+00 1005.4000000 0.61921576E+00 0.60448211E+00 1007.8000000 0.61885890E+00 0.60426419E+00 1010.2000000 0.61822951E+00 0.60405920E+00 1012.6000000 0.61735762E+00 0.60386838E+00 1015.0000000 0.61627330E+00 0.60369299E+00 1017.4000000 0.61500658E+00 0.60353430E+00 1019.8000000 0.61358750E+00 0.60339355E+00 1022.2000000 0.61204611E+00 0.60327201E+00 1024.6000000 0.61041245E+00 0.60317093E+00 1027.0000000 0.60871657E+00 0.60309156E+00 1029.4000000 0.60698851E+00 0.60303517E+00 1031.8000000 0.60525832E+00 0.60300302E+00 1034.2000000 0.60355603E+00 0.60299634E+00 1036.6000000 0.60191170E+00 0.60301641E+00 1039.0000000 0.60035537E+00 0.60306449E+00 1041.4000000 0.59891707E+00 0.60314181E+00 1043.8000000 0.59762687E+00 0.60324965E+00 1046.2000000 0.59651479E+00 0.60338927E+00 1048.6000000 0.59561088E+00 0.60356190E+00 1051.0000000 0.59494520E+00 0.60376882E+00 1053.4000000 0.59454777E+00 0.60401128E+00 1055.8000000 0.59444865E+00 0.60429053E+00 1058.2000000 0.59467788E+00 0.60460784E+00 1060.6000000 0.59526551E+00 0.60496446E+00 1063.0000000 0.59624157E+00 0.60536164E+00 1065.4000000 0.59763612E+00 0.60580064E+00 1067.8000000 0.59947919E+00 0.60628272E+00 1070.2000000 0.60180083E+00 0.60680914E+00 1072.6000000 0.60463109E+00 0.60738114E+00 1075.0000000 0.60800000E+00 0.60800000E+00 TEST18 'natural' parametrization x y 0.2000000 0.0100000 0.2100000 0.0081000 0.2200000 0.0064000 0.2300000 0.0049000 0.2400000 0.0036000 0.2500000 0.0025000 0.2600000 0.0016000 0.2700000 0.0009000 0.2800000 0.0004000 0.2900000 0.0001000 0.3000000 0.0000000 0.3100000 0.0001000 0.3200000 0.0004000 0.3300000 0.0009000 0.3400000 0.0016000 0.3500000 0.0025000 0.3600000 0.0036000 0.3700000 0.0049000 0.3800000 0.0064000 0.3900000 0.0081000 0.4000000 0.0100000 'uniform' parametrization x y 0.2000000 0.0100000 0.2181472 0.0074095 0.2365974 0.0052868 0.2544417 0.0035785 0.2707713 0.0022314 0.2846773 0.0011923 0.2952510 0.0004078 0.3015980 -0.0001750 0.3036973 -0.0005893 0.3028813 -0.0008378 0.3005987 -0.0009205 0.2982983 -0.0008374 0.2974290 -0.0005886 0.2994395 -0.0001740 0.3056627 0.0004089 0.3160850 0.0011933 0.3298237 0.0022323 0.3459816 0.0035792 0.3636617 0.0052872 0.3819669 0.0074097 0.4000000 0.0100000 TEST19 given data 1.0 2.0 3.0 4.0 5.0 6.0 1.0 0.00000E+00 0.00000E+00 0.00000E+00 0.10000E+01 0.80000E+01 0.27000E+02 2.0 0.00000E+00 0.00000E+00 0.00000E+00 0.10000E+01 0.80000E+01 0.27000E+02 3.0 0.00000E+00 0.00000E+00 0.00000E+00 0.10000E+01 0.80000E+01 0.27000E+02 4.0 0.25000E+00 0.25000E+00 0.25000E+00 0.12500E+01 0.82500E+01 0.27250E+02 5.0 0.22500E+01 0.22500E+01 0.22500E+01 0.32500E+01 0.10250E+02 0.29250E+02 6.0 0.62500E+01 0.62500E+01 0.62500E+01 0.72500E+01 0.14250E+02 0.33250E+02 7.0 0.12250E+02 0.12250E+02 0.12250E+02 0.13250E+02 0.20250E+02 0.39250E+02 interpolation error 1.0 2.0 3.0 4.0 5.0 6.0 1.0 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 2.0 0.00000E+00 0.77037E-33 0.41087E-32 0.00000E+00 0.00000E+00 0.00000E+00 3.0-0.38519E-33-0.15407E-32-0.82173E-32 0.00000E+00 0.00000E+00 0.00000E+00 4.0 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00-0.35527E-14 5.0 0.00000E+00 0.00000E+00 0.00000E+00 0.44409E-15 0.00000E+00 0.00000E+00 6.0 0.00000E+00-0.17764E-14 0.00000E+00 0.00000E+00-0.35527E-14 0.00000E+00 7.0 0.00000E+00-0.17764E-14 0.00000E+00-0.17764E-14 0.00000E+00 0.00000E+00 TEST20 given data 1.0 2.0 3.0 4.0 5.0 6.0 1.0 0.00000E+00 0.00000E+00 0.00000E+00 0.10000E+01 0.80000E+01 0.27000E+02 2.0 0.00000E+00 0.00000E+00 0.00000E+00 0.10000E+01 0.80000E+01 0.27000E+02 3.0 0.00000E+00 0.00000E+00 0.00000E+00 0.10000E+01 0.80000E+01 0.27000E+02 4.0 0.25000E+00 0.25000E+00 0.25000E+00 0.12500E+01 0.82500E+01 0.27250E+02 5.0 0.22500E+01 0.22500E+01 0.22500E+01 0.32500E+01 0.10250E+02 0.29250E+02 6.0 0.62500E+01 0.62500E+01 0.62500E+01 0.72500E+01 0.14250E+02 0.33250E+02 7.0 0.12250E+02 0.12250E+02 0.12250E+02 0.13250E+02 0.20250E+02 0.39250E+02 interpolation error 1.0 2.0 3.0 4.0 5.0 6.0 1.0 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 2.0 0.00000E+00 0.00000E+00 0.38519E-32-0.22204E-15-0.17764E-14-0.10658E-13 3.0 0.00000E+00 0.00000E+00-0.61630E-32 0.11102E-15-0.17764E-14-0.10658E-13 4.0 0.00000E+00 0.27756E-16 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 5.0 0.00000E+00 0.00000E+00 0.44409E-15 0.88818E-15-0.53291E-14-0.28422E-13 6.0 0.00000E+00 0.00000E+00 0.00000E+00-0.88818E-15-0.35527E-14-0.71054E-14 7.0 0.00000E+00 0.00000E+00 0.35527E-14 0.00000E+00 0.35527E-14 0.28422E-13 TEST21 approximation by splines of order 2 on 6 intervals. breakpoints - 0.1666666667E+00 0.3333333333E+00 0.5000000000E+00 0.6666666667E+00 0.8333333333E+00 least square error = 0.116995E-02 average error = 0.856121E-03 maximum error = 0.243739E-02 approximation by splines of order 2 on 6 intervals. breakpoints - 0.1219203049E+00 0.2394269580E+00 0.3540956825E+00 0.4675199446E+00 0.6163533526E+00 least square error = 0.485002E-02 average error = 0.372762E-02 maximum error = 0.999725E-02 approximation by splines of order 3 on 1 intervals. breakpoints - least square error = 0.460310E+00 average error = 0.391244E+00 maximum error = 0.134714E+01 approximation by splines of order 3 on 1 intervals. breakpoints - least square error = 0.460310E+00 average error = 0.391244E+00 maximum error = 0.134714E+01 approximation by splines of order 3 on 2 intervals. breakpoints - 0.1500000000E+01 least square error = 0.121451E+00 average error = 0.913469E-01 maximum error = 0.428157E+00 approximation by splines of order 3 on 3 intervals. breakpoints - 0.1000000000E+01 0.2000000000E+01 least square error = 0.385040E-01 average error = 0.276762E-01 maximum error = 0.138238E+00 approximation by splines of order 3 on 4 intervals. breakpoints - 0.7500000000E+00 0.1500000000E+01 0.2250000000E+01 least square error = 0.171150E-01 average error = 0.123528E-01 maximum error = 0.589345E-01 approximation by splines of order 3 on 5 intervals. breakpoints - 0.6000000000E+00 0.1200000000E+01 0.1800000000E+01 0.2400000000E+01 least square error = 0.938277E-02 average error = 0.696340E-02 maximum error = 0.291671E-01 approximation by splines of order 3 on 6 intervals. breakpoints - 0.5000000000E+00 0.1000000000E+01 0.1500000000E+01 0.2000000000E+01 0.2500000000E+01 least square error = 0.526016E-02 average error = 0.396308E-02 maximum error = 0.160495E-01 approximation by splines of order 3 on 7 intervals. breakpoints - 0.4285714286E+00 0.8571428571E+00 0.1285714286E+01 0.1714285714E+01 0.2142857143E+01 0.2571428571E+01 least square error = 0.419508E-02 average error = 0.330550E-02 maximum error = 0.104223E-01 approximation by splines of order 3 on 8 intervals. breakpoints - 0.3750000000E+00 0.7500000000E+00 0.1125000000E+01 0.1500000000E+01 0.1875000000E+01 0.2250000000E+01 0.2625000000E+01 least square error = 0.369242E-02 average error = 0.289470E-02 maximum error = 0.102887E-01 approximation by splines of order 3 on 9 intervals. breakpoints - 0.3333333333E+00 0.6666666667E+00 0.1000000000E+01 0.1333333333E+01 0.1666666667E+01 0.2000000000E+01 0.2333333333E+01 0.2666666667E+01 least square error = 0.319237E-02 average error = 0.256675E-02 maximum error = 0.737150E-02 approximation by splines of order 3 on 10 intervals. breakpoints - 0.3000000000E+00 0.6000000000E+00 0.9000000000E+00 0.1200000000E+01 0.1500000000E+01 0.1800000000E+01 0.2100000000E+01 0.2400000000E+01 0.2700000000E+01 least square error = 0.287403E-02 average error = 0.247918E-02 maximum error = 0.613093E-02 approximation by splines of order 3 on 11 intervals. breakpoints - 0.2727272727E+00 0.5454545455E+00 0.8181818182E+00 0.1090909091E+01 0.1363636364E+01 0.1636363636E+01 0.1909090909E+01 0.2181818182E+01 0.2454545455E+01 0.2727272727E+01 least square error = 0.270043E-02 average error = 0.230457E-02 maximum error = 0.578737E-02 approximation by splines of order 3 on 12 intervals. breakpoints - 0.2500000000E+00 0.5000000000E+00 0.7500000000E+00 0.1000000000E+01 0.1250000000E+01 0.1500000000E+01 0.1750000000E+01 0.2000000000E+01 0.2250000000E+01 0.2500000000E+01 0.2750000000E+01 least square error = 0.260370E-02 average error = 0.224555E-02 maximum error = 0.574599E-02 approximation by splines of order 3 on 13 intervals. breakpoints - 0.2307692308E+00 0.4615384615E+00 0.6923076923E+00 0.9230769231E+00 0.1153846154E+01 0.1384615385E+01 0.1615384615E+01 0.1846153846E+01 0.2076923077E+01 0.2307692308E+01 0.2538461538E+01 0.2769230769E+01 least square error = 0.271116E-02 average error = 0.234604E-02 maximum error = 0.611600E-02 approximation by splines of order 3 on 14 intervals. breakpoints - 0.2142857143E+00 0.4285714286E+00 0.6428571429E+00 0.8571428571E+00 0.1071428571E+01 0.1285714286E+01 0.1500000000E+01 0.1714285714E+01 0.1928571429E+01 0.2142857143E+01 0.2357142857E+01 0.2571428571E+01 0.2785714286E+01 least square error = 0.268365E-02 average error = 0.224667E-02 maximum error = 0.628692E-02 approximation by splines of order 3 on 15 intervals. breakpoints - 0.2000000000E+00 0.4000000000E+00 0.6000000000E+00 0.8000000000E+00 0.1000000000E+01 0.1200000000E+01 0.1400000000E+01 0.1600000000E+01 0.1800000000E+01 0.2000000000E+01 0.2200000000E+01 0.2400000000E+01 0.2600000000E+01 0.2800000000E+01 least square error = 0.252216E-02 average error = 0.211183E-02 maximum error = 0.571827E-02 approximation by splines of order 3 on 16 intervals. breakpoints - 0.1875000000E+00 0.3750000000E+00 0.5625000000E+00 0.7500000000E+00 0.9375000000E+00 0.1125000000E+01 0.1312500000E+01 0.1500000000E+01 0.1687500000E+01 0.1875000000E+01 0.2062500000E+01 0.2250000000E+01 0.2437500000E+01 0.2625000000E+01 0.2812500000E+01 least square error = 0.249301E-02 average error = 0.209679E-02 maximum error = 0.566659E-02 approximation by splines of order 3 on 17 intervals. breakpoints - 0.1764705882E+00 0.3529411765E+00 0.5294117647E+00 0.7058823529E+00 0.8823529412E+00 0.1058823529E+01 0.1235294118E+01 0.1411764706E+01 0.1588235294E+01 0.1764705882E+01 0.1941176471E+01 0.2117647059E+01 0.2294117647E+01 0.2470588235E+01 0.2647058824E+01 0.2823529412E+01 least square error = 0.245884E-02 average error = 0.206502E-02 maximum error = 0.587878E-02 approximation by splines of order 3 on 18 intervals. breakpoints - 0.1666666667E+00 0.3333333333E+00 0.5000000000E+00 0.6666666667E+00 0.8333333333E+00 0.1000000000E+01 0.1166666667E+01 0.1333333333E+01 0.1500000000E+01 0.1666666667E+01 0.1833333333E+01 0.2000000000E+01 0.2166666667E+01 0.2333333333E+01 0.2500000000E+01 0.2666666667E+01 0.2833333333E+01 least square error = 0.247271E-02 average error = 0.207767E-02 maximum error = 0.582376E-02 approximation by splines of order 3 on 19 intervals. breakpoints - 0.1578947368E+00 0.3157894737E+00 0.4736842105E+00 0.6315789474E+00 0.7894736842E+00 0.9473684211E+00 0.1105263158E+01 0.1263157895E+01 0.1421052632E+01 0.1578947368E+01 0.1736842105E+01 0.1894736842E+01 0.2052631579E+01 0.2210526316E+01 0.2368421053E+01 0.2526315789E+01 0.2684210526E+01 0.2842105263E+01 least square error = 0.246767E-02 average error = 0.205841E-02 maximum error = 0.554117E-02 approximation by splines of order 3 on 20 intervals. breakpoints - 0.1500000000E+00 0.3000000000E+00 0.4500000000E+00 0.6000000000E+00 0.7500000000E+00 0.9000000000E+00 0.1050000000E+01 0.1200000000E+01 0.1350000000E+01 0.1500000000E+01 0.1650000000E+01 0.1800000000E+01 0.1950000000E+01 0.2100000000E+01 0.2250000000E+01 0.2400000000E+01 0.2550000000E+01 0.2700000000E+01 0.2850000000E+01 least square error = 0.240785E-02 average error = 0.202511E-02 maximum error = 0.555014E-02 approximation by splines of order 5 on 8 intervals. breakpoints - 0.7309850000E+03 0.7944140000E+03 0.8444760000E+03 0.8800600000E+03 0.9078140000E+03 0.9380010000E+03 0.9767520000E+03 least square error = 0.555261E-01 average error = 0.361613E-01 maximum error = 0.215728E+00 approximation by splines of order 5 on 8 intervals. breakpoints - 0.6871177453E+03 0.7657269388E+03 0.8200865287E+03 0.8605900950E+03 0.8942118412E+03 0.9276762306E+03 0.9705628396E+03 least square error = 0.987152E-01 average error = 0.686795E-01 maximum error = 0.316400E+00 approximation by splines of order 5 on 10 intervals. breakpoints - 0.6672842404E+03 0.7327493103E+03 0.7889028955E+03 0.8365926385E+03 0.8794012607E+03 0.9157390089E+03 0.9513765096E+03 0.9904679899E+03 0.1032733995E+04 least square error = 0.585322E-01 average error = 0.367868E-01 maximum error = 0.214116E+00 approximation by splines of order 5 on 12 intervals. breakpoints - 0.6544354490E+03 0.7121000744E+03 0.7627219684E+03 0.8050423948E+03 0.8407039744E+03 0.8709303781E+03 0.8993400905E+03 0.9274230238E+03 0.9568547424E+03 0.9903625043E+03 0.1031447166E+04 least square error = 0.568376E-01 average error = 0.371164E-01 maximum error = 0.188978E+00 approximation by splines of order 5 on 14 intervals. breakpoints - 0.6461689199E+03 0.6976098897E+03 0.7453688503E+03 0.7853338102E+03 0.8180710057E+03 0.8460563774E+03 0.8716870303E+03 0.8999556724E+03 0.9280764209E+03 0.9531830320E+03 0.9801340324E+03 0.1010060088E+04 0.1042043552E+04 least square error = 0.449888E-01 average error = 0.274609E-01 maximum error = 0.165889E+00 PPPACK_PRB Normal end of execution. 25 March 2017 10:05:30.851 AM