###------------------------------------------------------------------------------------------ PROGRAM : NIP.pl Version 0.1 FILE NAME : NIP_output_StudyCase_4_sqrt_2.txt CONTENTS : Results of NEWTON INTERPOLATION POLYNOMIALS AUTHOR : Amar Khelil, www.khelil.de, 2015, All rights reserved ###------------------------------------------------------------------------------------------ Starts processing : Tue Jun 9 01:24:13 2015 ...................................................................... Function: show_Input_Data ...................................................................... Number of measures n : [ 11] X0 (first measure) : [ 0.000] Delta_X (xi+1 - xi), i=0,n-1 : [ 0.200] (X,Y)[ 0] : ( 0.000, 0.000000000) (X,Y)[ 1] : ( 0.200, 0.447213596) (X,Y)[ 2] : ( 0.400, 0.632455532) (X,Y)[ 3] : ( 0.600, 0.774596669) (X,Y)[ 4] : ( 0.800, 0.894427191) (X,Y)[ 5] : ( 1.000, 1.000000000) (X,Y)[ 6] : ( 1.200, 1.095445115) (X,Y)[ 7] : ( 1.400, 1.183215957) (X,Y)[ 8] : ( 1.600, 1.264911064) (X,Y)[ 9] : ( 1.800, 1.341640786) (X,Y)[ 10] : ( 2.000, 1.414213562) ...................................................................... Function: show_b_coeff_1 ...................................................................... Number of measures : [ 11] X0 : [ 0.000] Delta_X : [ 0.200] Xmax : [ 2.000] Values of the b-coefficients of the NIP Beware: They differ from the c-coefficients of the same polynomial in canonical form. b 0 : +0.0000000000 b 1 : +2.2360679775 b 2 : -3.2746457375 b 3 : +4.5598095771 b 4 : -5.1583509323 b 5 : +4.8266508984 b 6 : -3.8309244141 b 7 : +2.6345623310 b 8 : -1.5967701929 b 9 : +0.8646288756 b10 : -0.4229517514 ...................................................................... Function: show_Analysis_Data ...................................................................... Name of interpolated function : [SQRT(X)] Number of calculated points n : [ 42] X0 (first calculated point) : [ 0.000] Delta_X (xi+1 - xi), i=0,n-1 : [ 0.100] Number of NIPs considered : [ 2] (e.g. max. b coefficient taken) n of bmax[ 0] : [ 5] n of bmax[ 1] : [ 10] ---------------------------------------------------------------------- [ 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 : +0.0000000000 c 1 : +3.6887261304 c 2 : -10.2108662533 c 3 : +17.5071419536 c 4 : -14.8116527292 c 5 : +4.8266508984 ...................................................................... -3- Function: wri_Ys_NIP (output values of interpolation points) ...................................................................... b-coefficients b0 to b5 used: b 0 : +0.0000000000 b 1 : +2.2360679775 b 2 : -3.2746457375 b 3 : +4.5598095771 b 4 : -5.1583509323 b 5 : +4.8266508984 (X,Y) values (interpolated values) (X,Y)[ 0] : ( 0.000, 0.000000000) (X,Y)[ 1] : ( 0.100, 0.282838194) (X,Y)[ 2] : ( 0.200, 0.447213596) (X,Y)[ 3] : ( 0.300, 0.552087084) (X,Y)[ 4] : ( 0.400, 0.632455532) (X,Y)[ 5] : ( 0.500, 0.705143791) (X,Y)[ 6] : ( 0.600, 0.774596669) (X,Y)[ 7] : ( 0.700, 0.838670913) (X,Y)[ 8] : ( 0.800, 0.894427191) (X,Y)[ 9] : ( 0.900, 0.943922070) (X,Y)[ 10] : ( 1.000, 1.000000000) (X,Y)[ 11] : ( 1.100, 1.092085295) (X,Y)[ 12] : ( 1.200, 1.271974112) (X,Y)[ 13] : ( 1.300, 1.619626434) (X,Y)[ 14] : ( 1.400, 2.248958050) (X,Y)[ 15] : ( 1.500, 3.313632538) (X,Y)[ 16] : ( 1.600, 5.012853241) (X,Y)[ 17] : ( 1.700, 7.597155256) (X,Y)[ 18] : ( 1.800, 11.374197406) (X,Y)[ 19] : ( 1.900, 16.714554231) (X,Y)[ 20] : ( 2.000, 24.057507960) (X,Y)[ 21] : ( 2.100, 33.916840497) (X,Y)[ 22] : ( 2.200, 46.886625401) (X,Y)[ 23] : ( 2.300, 63.647019868) (X,Y)[ 24] : ( 2.400, 84.970056709) (X,Y)[ 25] : ( 2.500, 111.725436336) (X,Y)[ 26] : ( 2.600, 144.886318738) (X,Y)[ 27] : ( 2.700, 185.535115466) (X,Y)[ 28] : ( 2.800, 234.869281612) (X,Y)[ 29] : ( 2.900, 294.207107790) (X,Y)[ 30] : ( 3.000, 364.993512117) (X,Y)[ 31] : ( 3.100, 448.805832198) (X,Y)[ 32] : ( 3.200, 547.359617100) (X,Y)[ 33] : ( 3.300, 662.514419339) (X,Y)[ 34] : ( 3.400, 796.279586857) (X,Y)[ 35] : ( 3.500, 950.820055009) (X,Y)[ 36] : ( 3.600, 1128.462138535) (X,Y)[ 37] : ( 3.700, 1331.699323550) (X,Y)[ 38] : ( 3.800, 1563.198059520) (X,Y)[ 39] : ( 3.900, 1825.803551244) (X,Y)[ 40] : ( 4.000, 2122.545550835) (X,Y)[ 41] : ( 4.100, 2456.644149703) ---------------------------------------------------------------------- [ 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 : +0.0000000000 c 1 : +4.2280735342 c 2 : -17.0372885063 c 3 : +50.8437458399 c 4 : -98.8271330060 c 5 : +127.3064766291 c 6 : -109.6564207910 c 7 : +62.4351224588 c 8 : -22.5408190453 c 9 : +4.6711946380 c10 : -0.4229517514 ...................................................................... -3- Function: wri_Ys_NIP (output values of interpolation points) ...................................................................... b-coefficients b0 to b10 used: b 0 : +0.0000000000 b 1 : +2.2360679775 b 2 : -3.2746457375 b 3 : +4.5598095771 b 4 : -5.1583509323 b 5 : +4.8266508984 b 6 : -3.8309244141 b 7 : +2.6345623310 b 8 : -1.5967701929 b 9 : +0.8646288756 b10 : -0.4229517514 (X,Y) values (interpolated values) (X,Y)[ 0] : ( 0.000, 0.000000000) (X,Y)[ 1] : ( 0.100, 0.294564932) (X,Y)[ 2] : ( 0.200, 0.447213596) (X,Y)[ 3] : ( 0.300, 0.549027766) (X,Y)[ 4] : ( 0.400, 0.632455532) (X,Y)[ 5] : ( 0.500, 0.706867585) (X,Y)[ 6] : ( 0.600, 0.774596669) (X,Y)[ 7] : ( 0.700, 0.836741228) (X,Y)[ 8] : ( 0.800, 0.894427191) (X,Y)[ 9] : ( 0.900, 0.948639097) (X,Y)[ 10] : ( 1.000, 1.000000000) (X,Y)[ 11] : ( 1.100, 1.048845274) (X,Y)[ 12] : ( 1.200, 1.095445115) (X,Y)[ 13] : ( 1.300, 1.140130675) (X,Y)[ 14] : ( 1.400, 1.183215957) (X,Y)[ 15] : ( 1.500, 1.224828300) (X,Y)[ 16] : ( 1.600, 1.264911064) (X,Y)[ 17] : ( 1.700, 1.303589443) (X,Y)[ 18] : ( 1.800, 1.341640786) (X,Y)[ 19] : ( 1.900, 1.379830849) (X,Y)[ 20] : ( 2.000, 1.414213562) (X,Y)[ 21] : ( 2.100, 1.421990762) (X,Y)[ 22] : ( 2.200, 1.329036279) (X,Y)[ 23] : ( 2.300, 0.945552532) (X,Y)[ 24] : ( 2.400, -0.149606391) (X,Y)[ 25] : ( 2.500, -2.802796512) (X,Y)[ 26] : ( 2.600, -8.593472098) (X,Y)[ 27] : ( 2.700, -20.302689999) (X,Y)[ 28] : ( 2.800, -42.601480128) (X,Y)[ 29] : ( 2.900, -83.033057254) (X,Y)[ 30] : ( 3.000, -153.379793275) (X,Y)[ 31] : ( 3.100, -271.525185194) (X,Y)[ 32] : ( 3.200, -463.942895778) (X,Y)[ 33] : ( 3.300, -768.969464747) (X,Y)[ 34] : ( 3.400, -1241.044641771) (X,Y)[ 35] : ( 3.500, -1956.133632102) (X,Y)[ 36] : ( 3.600, -3018.579024759) (X,Y)[ 37] : ( 3.700, -4569.666945314) (X,Y)[ 38] : ( 3.800, -6798.232193985) (X,Y)[ 39] : ( 3.900, -9953.670948408) (X,Y)[ 40] : ( 4.000, -14361.777182578) (X,Y)[ 41] : ( 4.100, -20443.870432580) ###------------------------------------------------------------------------------------------ Ends processing : Tue Jun 9 01:24:13 2015 ###------------------------------------------------------------------------------------------