###------------------------------------------------------------------------------------------ PROGRAM : NIP.pl Version 0.1 FILE NAME : NIP_output_StudyCase_2_exp_B.txt CONTENTS : Results of NEWTON INTERPOLATION POLYNOMIALS AUTHOR : Amar Khelil, www.khelil.de, 2015, All rights reserved ###------------------------------------------------------------------------------------------ Starts processing : Tue Jun 9 01:19:55 2015 ...................................................................... Function: show_Input_Data ...................................................................... Number of measures n : [ 15] X0 (first measure) : [ 0.000] Delta_X (xi+1 - xi), i=0,n-1 : [ 0.400] (X,Y)[ 0] : ( 0.000, 1.000000000) (X,Y)[ 1] : ( 0.400, 1.491824698) (X,Y)[ 2] : ( 0.800, 2.225540929) (X,Y)[ 3] : ( 1.200, 3.320116923) (X,Y)[ 4] : ( 1.600, 4.953032424) (X,Y)[ 5] : ( 2.000, 7.389056099) (X,Y)[ 6] : ( 2.400, 11.023176381) (X,Y)[ 7] : ( 2.800, 16.444646771) (X,Y)[ 8] : ( 3.200, 24.532530197) (X,Y)[ 9] : ( 3.600, 36.598234444) (X,Y)[ 10] : ( 4.000, 54.598150033) (X,Y)[ 11] : ( 4.400, 81.450868665) (X,Y)[ 12] : ( 4.800, 121.510417519) (X,Y)[ 13] : ( 5.200, 181.272241875) (X,Y)[ 14] : ( 5.600, 270.426407426) ...................................................................... Function: show_b_coeff_1 ...................................................................... Number of measures : [ 15] X0 : [ 0.000] Delta_X : [ 0.400] Xmax : [ 5.600] Values of the b-coefficients of the NIP Beware: They differ from the c-coefficients of the same polynomial in canonical form. b 0 : +1.0000000000 b 1 : +1.2295617440 b 2 : +0.7559110416 b 3 : +0.3098130990 b 4 : +0.0952335843 b 5 : +0.0234191137 b 6 : +0.0047992083 b 7 : +0.0008429886 b 8 : +0.0001295635 b 9 : +0.0000177006 b10 : +0.0000021764 b11 : +0.0000002433 b12 : +0.0000000249 b13 : +0.0000000024 b14 : +0.0000000002 ...................................................................... Function: show_Analysis_Data ...................................................................... Name of interpolated function : [EXP(X)] Number of calculated points n : [ 50] X0 (first calculated point) : [ 0.000] Delta_X (xi+1 - xi), i=0,n-1 : [ 0.200] Number of NIPs considered : [ 3] (e.g. max. b coefficient taken) n of bmax[ 0] : [ 5] n of bmax[ 1] : [ 10] n of bmax[ 2] : [ 14] ---------------------------------------------------------------------- [ 0] ANALYSIS OF NIP=N5(x) ---------------------------------------------------------------------- ...................................................................... -1- Function: show_c_coeff (of NIP transposed into canonical form) .......................................................................................... c-coefficients of NIP=N 5(x) in canonical form: c 0 : +1.0000000000 c 1 : +1.0041565261 c 2 : +0.4768052674 c 3 : +0.2123995333 c 4 : +0.0015571296 c 5 : +0.0234191137 ...................................................................... -3- Function: wri_Ys_NIP (output values of interpolation points) ...................................................................... b-coefficients b0 to b5 used: b 0 : +1.0000000000 b 1 : +1.2295617440 b 2 : +0.7559110416 b 3 : +0.3098130990 b 4 : +0.0952335843 b 5 : +0.0234191137 (X,Y) values (interpolated values) (X,Y)[ 0] : ( 0.000, 1.000000000) (X,Y)[ 1] : ( 0.200, 1.221612698) (X,Y)[ 2] : ( 0.400, 1.491824698) (X,Y)[ 3] : ( 0.600, 1.822044985) (X,Y)[ 4] : ( 0.800, 2.225540929) (X,Y)[ 5] : ( 1.000, 2.718337570) (X,Y)[ 6] : ( 1.200, 3.320116923) (X,Y)[ 7] : ( 1.400, 4.055117263) (X,Y)[ 8] : ( 1.600, 4.953032424) (X,Y)[ 9] : ( 1.800, 6.049911093) (X,Y)[ 10] : ( 2.000, 7.389056099) (X,Y)[ 11] : ( 2.200, 9.021923713) (X,Y)[ 12] : ( 2.400, 11.009022939) (X,Y)[ 13] : ( 2.600, 13.420814809) (X,Y)[ 14] : ( 2.800, 16.338611674) (X,Y)[ 15] : ( 3.000, 19.855476504) (X,Y)[ 16] : ( 3.200, 24.077122174) (X,Y)[ 17] : ( 3.400, 29.122810765) (X,Y)[ 18] : ( 3.600, 35.126252856) (X,Y)[ 19] : ( 3.800, 42.236506815) (X,Y)[ 20] : ( 4.000, 50.618878095) (X,Y)[ 21] : ( 4.200, 60.455818531) (X,Y)[ 22] : ( 4.400, 71.947825629) (X,Y)[ 23] : ( 4.600, 85.314341861) (X,Y)[ 24] : ( 4.800, 100.794653963) (X,Y)[ 25] : ( 5.000, 118.648792223) (X,Y)[ 26] : ( 5.200, 139.158429779) (X,Y)[ 27] : ( 5.400, 162.627781914) (X,Y)[ 28] : ( 5.600, 189.384505345) (X,Y)[ 29] : ( 5.800, 219.780597520) (X,Y)[ 30] : ( 6.000, 254.193295914) (X,Y)[ 31] : ( 6.200, 293.025977319) (X,Y)[ 32] : ( 6.400, 336.709057141) (X,Y)[ 33] : ( 6.600, 385.700888691) (X,Y)[ 34] : ( 6.800, 440.488662481) (X,Y)[ 35] : ( 7.000, 501.589305520) (X,Y)[ 36] : ( 7.200, 569.550380603) (X,Y)[ 37] : ( 7.400, 644.950985608) (X,Y)[ 38] : ( 7.600, 728.402652791) (X,Y)[ 39] : ( 7.800, 820.550248077) (X,Y)[ 40] : ( 8.000, 922.072870356) (X,Y)[ 41] : ( 8.200, 1033.684750776) (X,Y)[ 42] : ( 8.400, 1156.136152038) (X,Y)[ 43] : ( 8.600, 1290.214267689) (X,Y)[ 44] : ( 8.800, 1436.744121417) (X,Y)[ 45] : ( 9.000, 1596.589466344) (X,Y)[ 46] : ( 9.200, 1770.653684319) (X,Y)[ 47] : ( 9.400, 1959.880685215) (X,Y)[ 48] : ( 9.600, 2165.255806220) (X,Y)[ 49] : ( 9.800, 2387.806711133) ---------------------------------------------------------------------- [ 1] ANALYSIS OF NIP=N10(x) ---------------------------------------------------------------------- ...................................................................... -1- Function: show_c_coeff (of NIP transposed into canonical form) .......................................................................................... c-coefficients of NIP=N10(x) in canonical form: c 0 : +1.0000000000 c 1 : +0.9999361463 c 2 : +0.5004629399 c 3 : +0.1652975971 c 4 : +0.0438795661 c 5 : +0.0061452376 c 6 : +0.0027799887 c 7 : -0.0003780932 c 8 : +0.0001776319 c 9 : -0.0000214749 c10 : +0.0000021764 ...................................................................... -3- Function: wri_Ys_NIP (output values of interpolation points) ...................................................................... b-coefficients b0 to b10 used: b 0 : +1.0000000000 b 1 : +1.2295617440 b 2 : +0.7559110416 b 3 : +0.3098130990 b 4 : +0.0952335843 b 5 : +0.0234191137 b 6 : +0.0047992083 b 7 : +0.0008429886 b 8 : +0.0001295635 b 9 : +0.0000177006 b10 : +0.0000021764 (X,Y) values (interpolated values) (X,Y)[ 0] : ( 0.000, 1.000000000) (X,Y)[ 1] : ( 0.200, 1.221400475) (X,Y)[ 2] : ( 0.400, 1.491824698) (X,Y)[ 3] : ( 0.600, 1.822119172) (X,Y)[ 4] : ( 0.800, 2.225540929) (X,Y)[ 5] : ( 1.000, 2.718281716) (X,Y)[ 6] : ( 1.200, 3.320116923) (X,Y)[ 7] : ( 1.400, 4.055200021) (X,Y)[ 8] : ( 1.600, 4.953032424) (X,Y)[ 9] : ( 1.800, 6.049647426) (X,Y)[ 10] : ( 2.000, 7.389056099) (X,Y)[ 11] : ( 2.200, 9.025013539) (X,Y)[ 12] : ( 2.400, 11.023176381) (X,Y)[ 13] : ( 2.600, 13.463737975) (X,Y)[ 14] : ( 2.800, 16.444646771) (X,Y)[ 15] : ( 3.000, 20.085537056) (X,Y)[ 16] : ( 3.200, 24.532530197) (X,Y)[ 17] : ( 3.400, 29.964099579) (X,Y)[ 18] : ( 3.600, 36.598234444) (X,Y)[ 19] : ( 3.800, 44.701187572) (X,Y)[ 20] : ( 4.000, 54.598150033) (X,Y)[ 21] : ( 4.200, 66.686263868) (X,Y)[ 22] : ( 4.400, 81.450461365) (X,Y)[ 23] : ( 4.600, 99.482708369) (X,Y)[ 24] : ( 4.800, 121.505329615) (X,Y)[ 25] : ( 5.000, 148.399207213) (X,Y)[ 26] : ( 5.200, 181.237769954) (X,Y)[ 27] : ( 5.400, 221.327831871) (X,Y)[ 28] : ( 5.600, 270.258494212) (X,Y)[ 29] : ( 5.800, 329.959496604) (X,Y)[ 30] : ( 6.000, 402.770591395) (X,Y)[ 31] : ( 6.200, 491.523720808) (X,Y)[ 32] : ( 6.400, 599.640000472) (X,Y)[ 33] : ( 6.600, 731.243755843) (X,Y)[ 34] : ( 6.800, 891.296120891) (X,Y)[ 35] : ( 7.000, 1085.750991916) (X,Y)[ 36] : ( 7.200, 1321.736434368) (X,Y)[ 37] : ( 7.400, 1607.764967848) (X,Y)[ 38] : ( 7.600, 1953.976504834) (X,Y)[ 39] : ( 7.800, 2372.418093020) (X,Y)[ 40] : ( 8.000, 2877.365010147) (X,Y)[ 41] : ( 8.200, 3485.688184789) (X,Y)[ 42] : ( 8.400, 4217.273367430) (X,Y)[ 43] : ( 8.600, 5095.497954221) (X,Y)[ 44] : ( 8.800, 6147.771871791) (X,Y)[ 45] : ( 9.000, 7406.149466263) (X,Y)[ 46] : ( 9.200, 8908.019903920) (X,Y)[ 47] : ( 9.400, 10696.884185720) (X,Y)[ 48] : ( 9.600, 12823.227503741) (X,Y)[ 49] : ( 9.800, 15345.496325531) ---------------------------------------------------------------------- [ 2] ANALYSIS OF NIP=N14(x) ---------------------------------------------------------------------- ...................................................................... -1- Function: show_c_coeff (of NIP transposed into canonical form) .......................................................................................... c-coefficients of NIP=N14(x) in canonical form: c 0 : +1.0000000000 c 1 : +0.9999973245 c 2 : +0.5000216050 c 3 : +0.1665925953 c 4 : +0.0418118925 c 5 : +0.0081494533 c 6 : +0.0015491374 c 7 : +0.0000987721 c 8 : +0.0000698567 c 9 : -0.0000121544 c10 : +0.0000038663 c11 : -0.0000005916 c12 : +0.0000000744 c13 : -0.0000000051 c14 : +0.0000000002 ...................................................................... -3- Function: wri_Ys_NIP (output values of interpolation points) ...................................................................... b-coefficients b0 to b14 used: b 0 : +1.0000000000 b 1 : +1.2295617440 b 2 : +0.7559110416 b 3 : +0.3098130990 b 4 : +0.0952335843 b 5 : +0.0234191137 b 6 : +0.0047992083 b 7 : +0.0008429886 b 8 : +0.0001295635 b 9 : +0.0000177006 b10 : +0.0000021764 b11 : +0.0000002433 b12 : +0.0000000249 b13 : +0.0000000024 b14 : +0.0000000002 (X,Y) values (interpolated values) (X,Y)[ 0] : ( 0.000, 1.000000000) (X,Y)[ 1] : ( 0.200, 1.221402677) (X,Y)[ 2] : ( 0.400, 1.491824698) (X,Y)[ 3] : ( 0.600, 1.822118810) (X,Y)[ 4] : ( 0.800, 2.225540929) (X,Y)[ 5] : ( 1.000, 2.718281827) (X,Y)[ 6] : ( 1.200, 3.320116923) (X,Y)[ 7] : ( 1.400, 4.055199967) (X,Y)[ 8] : ( 1.600, 4.953032424) (X,Y)[ 9] : ( 1.800, 6.049647464) (X,Y)[ 10] : ( 2.000, 7.389056099) (X,Y)[ 11] : ( 2.200, 9.025013500) (X,Y)[ 12] : ( 2.400, 11.023176381) (X,Y)[ 13] : ( 2.600, 13.463738035) (X,Y)[ 14] : ( 2.800, 16.444646771) (X,Y)[ 15] : ( 3.000, 20.085536923) (X,Y)[ 16] : ( 3.200, 24.532530197) (X,Y)[ 17] : ( 3.400, 29.964100047) (X,Y)[ 18] : ( 3.600, 36.598234444) (X,Y)[ 19] : ( 3.800, 44.701184494) (X,Y)[ 20] : ( 4.000, 54.598150033) (X,Y)[ 21] : ( 4.200, 66.686331040) (X,Y)[ 22] : ( 4.400, 81.450868665) (X,Y)[ 23] : ( 4.600, 99.484315644) (X,Y)[ 24] : ( 4.800, 121.510417519) (X,Y)[ 25] : ( 5.000, 148.413159090) (X,Y)[ 26] : ( 5.200, 181.272241875) (X,Y)[ 27] : ( 5.400, 221.406416321) (X,Y)[ 28] : ( 5.600, 270.426407426) (X,Y)[ 29] : ( 5.800, 330.299556442) (X,Y)[ 30] : ( 6.000, 403.428769184) (X,Y)[ 31] : ( 6.200, 492.748930785) (X,Y)[ 32] : ( 6.400, 601.844638358) (X,Y)[ 33] : ( 6.600, 735.093941747) (X,Y)[ 34] : ( 6.800, 897.843797523) (X,Y)[ 35] : ( 7.000, 1096.624166731) (X,Y)[ 36] : ( 7.200, 1339.409162612) (X,Y)[ 37] : ( 7.400, 1635.935426878) (X,Y)[ 38] : ( 7.600, 1998.090035828) (X,Y)[ 39] : ( 7.800, 2440.382772419) (X,Y)[ 40] : ( 8.000, 2980.520618267) (X,Y)[ 41] : ( 8.200, 3640.105901635) (X,Y)[ 42] : ( 8.400, 4445.483775935) (X,Y)[ 43] : ( 8.600, 5428.769703151) (X,Y)[ 44] : ( 8.800, 6629.093496266) (X,Y)[ 45] : ( 9.000, 8094.103367941) (X,Y)[ 46] : ( 9.200, 9881.781489625) (X,Y)[ 47] : ( 9.400, 12062.631954077) (X,Y)[ 48] : ( 9.600, 14722.312943254) (X,Y)[ 49] : ( 9.800, 17964.797541928) ###------------------------------------------------------------------------------------------ Ends processing : Tue Jun 9 01:19:55 2015 ###------------------------------------------------------------------------------------------