###------------------------------------------------------------------------------------------ PROGRAM : NIP.pl Version 0.1 FILE NAME : NIP_output_StudyCase_4_sqrt_1.txt CONTENTS : Results of NEWTON INTERPOLATION POLYNOMIALS AUTHOR : Amar Khelil, www.khelil.de, 2015, All rights reserved ###------------------------------------------------------------------------------------------ Starts processing : Tue Jun 9 01:22:56 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, 1.000000000) (X,Y)[ 1] : ( 0.200, 1.095445115) (X,Y)[ 2] : ( 0.400, 1.183215957) (X,Y)[ 3] : ( 0.600, 1.264911064) (X,Y)[ 4] : ( 0.800, 1.341640786) (X,Y)[ 5] : ( 1.000, 1.414213562) (X,Y)[ 6] : ( 1.200, 1.483239697) (X,Y)[ 7] : ( 1.400, 1.549193338) (X,Y)[ 8] : ( 1.600, 1.612451550) (X,Y)[ 9] : ( 1.800, 1.673320053) (X,Y)[ 10] : ( 2.000, 1.732050808) ...................................................................... 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 : +1.0000000000 b 1 : +0.4772255750 b 2 : -0.0959284175 b 3 : +0.0333029021 b 4 : -0.0127132891 b 5 : +0.0048510391 b 6 : -0.0017904188 b 7 : +0.0006308826 b 8 : -0.0002111555 b 9 : +0.0000670386 b10 : -0.0000202043 ...................................................................... Function: show_Analysis_Data ...................................................................... Name of interpolated function : [SQRT(X+1)] 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 : +1.0000000000 c 1 : +0.4998720084 c 2 : -0.1234444216 c 3 : +0.0553503036 c 4 : -0.0224153672 c 5 : +0.0048510391 ...................................................................... -3- Function: wri_Ys_NIP (output values of interpolation points) ...................................................................... b-coefficients b0 to b5 used: b 0 : +1.0000000000 b 1 : +0.4772255750 b 2 : -0.0959284175 b 3 : +0.0333029021 b 4 : -0.0127132891 b 5 : +0.0048510391 (X,Y) values (interpolated values) (X,Y)[ 0] : ( 0.000, 1.000000000) (X,Y)[ 1] : ( 0.100, 1.048805914) (X,Y)[ 2] : ( 0.200, 1.095445115) (X,Y)[ 3] : ( 0.300, 1.140176286) (X,Y)[ 4] : ( 0.400, 1.183215957) (X,Y)[ 5] : ( 0.500, 1.224744321) (X,Y)[ 6] : ( 0.600, 1.264911064) (X,Y)[ 7] : ( 0.700, 1.303841178) (X,Y)[ 8] : ( 0.800, 1.341640786) (X,Y)[ 9] : ( 0.900, 1.378402965) (X,Y)[ 10] : ( 1.000, 1.414213562) (X,Y)[ 11] : ( 1.100, 1.449157021) (X,Y)[ 12] : ( 1.200, 1.483322200) (X,Y)[ 13] : ( 1.300, 1.516808194) (X,Y)[ 14] : ( 1.400, 1.549730157) (X,Y)[ 15] : ( 1.500, 1.582225120) (X,Y)[ 16] : ( 1.600, 1.614457819) (X,Y)[ 17] : ( 1.700, 1.646626507) (X,Y)[ 18] : ( 1.800, 1.678968783) (X,Y)[ 19] : ( 1.900, 1.711767410) (X,Y)[ 20] : ( 2.000, 1.745356135) (X,Y)[ 21] : ( 2.100, 1.780125513) (X,Y)[ 22] : ( 2.200, 1.816528727) (X,Y)[ 23] : ( 2.300, 1.855087410) (X,Y)[ 24] : ( 2.400, 1.896397464) (X,Y)[ 25] : ( 2.500, 1.941134883) (X,Y)[ 26] : ( 2.600, 1.990061576) (X,Y)[ 27] : ( 2.700, 2.044031185) (X,Y)[ 28] : ( 2.800, 2.103994905) (X,Y)[ 29] : ( 2.900, 2.171007313) (X,Y)[ 30] : ( 3.000, 2.246232180) (X,Y)[ 31] : ( 3.100, 2.330948297) (X,Y)[ 32] : ( 3.200, 2.426555297) (X,Y)[ 33] : ( 3.300, 2.534579474) (X,Y)[ 34] : ( 3.400, 2.656679604) (X,Y)[ 35] : ( 3.500, 2.794652768) (X,Y)[ 36] : ( 3.600, 2.950440174) (X,Y)[ 37] : ( 3.700, 3.126132974) (X,Y)[ 38] : ( 3.800, 3.323978090) (X,Y)[ 39] : ( 3.900, 3.546384032) (X,Y)[ 40] : ( 4.000, 3.795926722) (X,Y)[ 41] : ( 4.100, 4.075355313) ---------------------------------------------------------------------- [ 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 : +0.4999941272 c 2 : -0.1249091931 c 3 : +0.0619097542 c 4 : -0.0368784515 c 5 : +0.0220985976 c 6 : -0.0116379230 c 7 : +0.0048049210 c 8 : -0.0013969429 c 9 : +0.0002488773 c10 : -0.0000202043 ...................................................................... -3- Function: wri_Ys_NIP (output values of interpolation points) ...................................................................... b-coefficients b0 to b10 used: b 0 : +1.0000000000 b 1 : +0.4772255750 b 2 : -0.0959284175 b 3 : +0.0333029021 b 4 : -0.0127132891 b 5 : +0.0048510391 b 6 : -0.0017904188 b 7 : +0.0006308826 b 8 : -0.0002111555 b 9 : +0.0000670386 b10 : -0.0000202043 (X,Y) values (interpolated values) (X,Y)[ 0] : ( 0.000, 1.000000000) (X,Y)[ 1] : ( 0.100, 1.048808753) (X,Y)[ 2] : ( 0.200, 1.095445115) (X,Y)[ 3] : ( 0.300, 1.140175438) (X,Y)[ 4] : ( 0.400, 1.183215957) (X,Y)[ 5] : ( 0.500, 1.224744868) (X,Y)[ 6] : ( 0.600, 1.264911064) (X,Y)[ 7] : ( 0.700, 1.303840482) (X,Y)[ 8] : ( 0.800, 1.341640786) (X,Y)[ 9] : ( 0.900, 1.378404874) (X,Y)[ 10] : ( 1.000, 1.414213562) (X,Y)[ 11] : ( 1.100, 1.449137675) (X,Y)[ 12] : ( 1.200, 1.483239697) (X,Y)[ 13] : ( 1.300, 1.516575088) (X,Y)[ 14] : ( 1.400, 1.549193338) (X,Y)[ 15] : ( 1.500, 1.581138832) (X,Y)[ 16] : ( 1.600, 1.612451550) (X,Y)[ 17] : ( 1.700, 1.643167666) (X,Y)[ 18] : ( 1.800, 1.673320053) (X,Y)[ 19] : ( 1.900, 1.702938678) (X,Y)[ 20] : ( 2.000, 1.732050808) (X,Y)[ 21] : ( 2.100, 1.760680866) (X,Y)[ 22] : ( 2.200, 1.788849645) (X,Y)[ 23] : ( 2.300, 1.816572405) (X,Y)[ 24] : ( 2.400, 1.843855164) (X,Y)[ 25] : ( 2.500, 1.870688209) (X,Y)[ 26] : ( 2.600, 1.897035486) (X,Y)[ 27] : ( 2.700, 1.922818123) (X,Y)[ 28] : ( 2.800, 1.947889799) (X,Y)[ 29] : ( 2.900, 1.972001109) (X,Y)[ 30] : ( 3.000, 1.994749348) (X,Y)[ 31] : ( 3.100, 2.015509358) (X,Y)[ 32] : ( 3.200, 2.033340160) (X,Y)[ 33] : ( 3.300, 2.046861068) (X,Y)[ 34] : ( 3.400, 2.054089821) (X,Y)[ 35] : ( 3.500, 2.052234000) (X,Y)[ 36] : ( 3.600, 2.037425525) (X,Y)[ 37] : ( 3.700, 2.004386505) (X,Y)[ 38] : ( 3.800, 1.946012930) (X,Y)[ 39] : ( 3.900, 1.852860835) (X,Y)[ 40] : ( 4.000, 1.712517481) (X,Y)[ 41] : ( 4.100, 1.508837861) ###------------------------------------------------------------------------------------------ Ends processing : Tue Jun 9 01:22:56 2015 ###------------------------------------------------------------------------------------------