###------------------------------------------------------------------------------------------ PROGRAM : NIP.pl Version 0.1 FILE NAME : NIP_output_StudyCase_1_Polynomial.txt CONTENTS : Results of NEWTON INTERPOLATION POLYNOMIALS AUTHOR : Amar Khelil, www.khelil.de, 2015, All rights reserved ###------------------------------------------------------------------------------------------ Starts processing : Tue Jun 9 01:18:07 2015 ...................................................................... Function: show_Input_Data ...................................................................... Number of measures n : [ 10] X0 (first measure) : [ 0.000] Delta_X (xi+1 - xi), i=0,n-1 : [ 0.100] (X,Y)[ 0] : ( 0.000, 1.000000000) (X,Y)[ 1] : ( 0.100, 1.105270000) (X,Y)[ 2] : ( 0.200, 1.222640000) (X,Y)[ 3] : ( 0.300, 1.356610000) (X,Y)[ 4] : ( 0.400, 1.516480000) (X,Y)[ 5] : ( 0.500, 1.718750000) (X,Y)[ 6] : ( 0.600, 1.989520000) (X,Y)[ 7] : ( 0.700, 2.366890000) (X,Y)[ 8] : ( 0.800, 2.903360000) (X,Y)[ 9] : ( 0.900, 3.668230000) ...................................................................... Function: show_b_coeff_1 ...................................................................... Number of measures : [ 10] X0 : [ 0.000] Delta_X : [ 0.100] Xmax : [ 0.900] 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 : +1.0527000000 b 2 : +0.6050000000 b 3 : +0.7500000000 b 4 : +2.0000000000 b 5 : +2.0000000000 b 6 : +0.0000000000 b 7 : -0.0000000000 b 8 : +0.0000000000 b 9 : -0.0000000000 ...................................................................... Function: show_Analysis_Data ...................................................................... Name of interpolated function : [1 + X + 0.5 X**2 + 0.25 X**3 + 2 X**5] Number of calculated points n : [ 41] X0 (first calculated point) : [ 0.000] Delta_X (xi+1 - xi), i=0,n-1 : [ 0.050] Number of NIPs considered : [ 2] (e.g. max. b coefficient taken) n of bmax[ 0] : [ 5] n of bmax[ 1] : [ 9] ---------------------------------------------------------------------- [ 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 : +1.0000000000 c 2 : +0.5000000000 c 3 : +0.2500000000 c 4 : +0.0000000000 c 5 : +2.0000000000 ...................................................................... -3- Function: wri_Ys_NIP (output values of interpolation points) ...................................................................... b-coefficients b0 to b5 used: b 0 : +1.0000000000 b 1 : +1.0527000000 b 2 : +0.6050000000 b 3 : +0.7500000000 b 4 : +2.0000000000 b 5 : +2.0000000000 (X,Y) values (interpolated values) (X,Y)[ 0] : ( 0.000, 1.000000000) (X,Y)[ 1] : ( 0.050, 1.051281875) (X,Y)[ 2] : ( 0.100, 1.105270000) (X,Y)[ 3] : ( 0.150, 1.162245625) (X,Y)[ 4] : ( 0.200, 1.222640000) (X,Y)[ 5] : ( 0.250, 1.287109375) (X,Y)[ 6] : ( 0.300, 1.356610000) (X,Y)[ 7] : ( 0.350, 1.432473125) (X,Y)[ 8] : ( 0.400, 1.516480000) (X,Y)[ 9] : ( 0.450, 1.610936875) (X,Y)[ 10] : ( 0.500, 1.718750000) (X,Y)[ 11] : ( 0.550, 1.843500625) (X,Y)[ 12] : ( 0.600, 1.989520000) (X,Y)[ 13] : ( 0.650, 2.161964375) (X,Y)[ 14] : ( 0.700, 2.366890000) (X,Y)[ 15] : ( 0.750, 2.611328125) (X,Y)[ 16] : ( 0.800, 2.903360000) (X,Y)[ 17] : ( 0.850, 3.252191875) (X,Y)[ 18] : ( 0.900, 3.668230000) (X,Y)[ 19] : ( 0.950, 4.163155625) (X,Y)[ 20] : ( 1.000, 4.750000000) (X,Y)[ 21] : ( 1.050, 5.443219375) (X,Y)[ 22] : ( 1.100, 6.258770000) (X,Y)[ 23] : ( 1.150, 7.214183125) (X,Y)[ 24] : ( 1.200, 8.328640000) (X,Y)[ 25] : ( 1.250, 9.623046875) (X,Y)[ 26] : ( 1.300, 11.120110000) (X,Y)[ 27] : ( 1.350, 12.844410625) (X,Y)[ 28] : ( 1.400, 14.822480000) (X,Y)[ 29] : ( 1.450, 17.082874375) (X,Y)[ 30] : ( 1.500, 19.656250000) (X,Y)[ 31] : ( 1.550, 22.575438125) (X,Y)[ 32] : ( 1.600, 25.875520000) (X,Y)[ 33] : ( 1.650, 29.593901875) (X,Y)[ 34] : ( 1.700, 33.770390000) (X,Y)[ 35] : ( 1.750, 38.447265625) (X,Y)[ 36] : ( 1.800, 43.669360000) (X,Y)[ 37] : ( 1.850, 49.484129375) (X,Y)[ 38] : ( 1.900, 55.941730000) (X,Y)[ 39] : ( 1.950, 63.095093125) (X,Y)[ 40] : ( 2.000, 71.000000000) ---------------------------------------------------------------------- [ 1] ANALYSIS OF NIP=N9(x) ---------------------------------------------------------------------- ...................................................................... -1- Function: show_c_coeff (of NIP transposed into canonical form) .......................................................................................... c-coefficients of NIP=N 9(x) in canonical form: c 0 : +1.0000000000 c 1 : +1.0000000000 c 2 : +0.5000000000 c 3 : +0.2500000000 c 4 : +0.0000000000 c 5 : +1.9999999999 c 6 : +0.0000000002 c 7 : -0.0000000002 c 8 : +0.0000000001 c 9 : -0.0000000000 ...................................................................... -3- Function: wri_Ys_NIP (output values of interpolation points) ...................................................................... b-coefficients b0 to b9 used: b 0 : +1.0000000000 b 1 : +1.0527000000 b 2 : +0.6050000000 b 3 : +0.7500000000 b 4 : +2.0000000000 b 5 : +2.0000000000 b 6 : +0.0000000000 b 7 : -0.0000000000 b 8 : +0.0000000000 b 9 : -0.0000000000 (X,Y) values (interpolated values) (X,Y)[ 0] : ( 0.000, 1.000000000) (X,Y)[ 1] : ( 0.050, 1.051281875) (X,Y)[ 2] : ( 0.100, 1.105270000) (X,Y)[ 3] : ( 0.150, 1.162245625) (X,Y)[ 4] : ( 0.200, 1.222640000) (X,Y)[ 5] : ( 0.250, 1.287109375) (X,Y)[ 6] : ( 0.300, 1.356610000) (X,Y)[ 7] : ( 0.350, 1.432473125) (X,Y)[ 8] : ( 0.400, 1.516480000) (X,Y)[ 9] : ( 0.450, 1.610936875) (X,Y)[ 10] : ( 0.500, 1.718750000) (X,Y)[ 11] : ( 0.550, 1.843500625) (X,Y)[ 12] : ( 0.600, 1.989520000) (X,Y)[ 13] : ( 0.650, 2.161964375) (X,Y)[ 14] : ( 0.700, 2.366890000) (X,Y)[ 15] : ( 0.750, 2.611328125) (X,Y)[ 16] : ( 0.800, 2.903360000) (X,Y)[ 17] : ( 0.850, 3.252191875) (X,Y)[ 18] : ( 0.900, 3.668230000) (X,Y)[ 19] : ( 0.950, 4.163155625) (X,Y)[ 20] : ( 1.000, 4.750000000) (X,Y)[ 21] : ( 1.050, 5.443219375) (X,Y)[ 22] : ( 1.100, 6.258770000) (X,Y)[ 23] : ( 1.150, 7.214183125) (X,Y)[ 24] : ( 1.200, 8.328640000) (X,Y)[ 25] : ( 1.250, 9.623046875) (X,Y)[ 26] : ( 1.300, 11.120110000) (X,Y)[ 27] : ( 1.350, 12.844410625) (X,Y)[ 28] : ( 1.400, 14.822480000) (X,Y)[ 29] : ( 1.450, 17.082874375) (X,Y)[ 30] : ( 1.500, 19.656250000) (X,Y)[ 31] : ( 1.550, 22.575438125) (X,Y)[ 32] : ( 1.600, 25.875520000) (X,Y)[ 33] : ( 1.650, 29.593901875) (X,Y)[ 34] : ( 1.700, 33.770390000) (X,Y)[ 35] : ( 1.750, 38.447265625) (X,Y)[ 36] : ( 1.800, 43.669360000) (X,Y)[ 37] : ( 1.850, 49.484129375) (X,Y)[ 38] : ( 1.900, 55.941730000) (X,Y)[ 39] : ( 1.950, 63.095093125) (X,Y)[ 40] : ( 2.000, 71.000000000) ###------------------------------------------------------------------------------------------ Ends processing : Tue Jun 9 01:18:07 2015 ###------------------------------------------------------------------------------------------