Chebyshev coefficients

Chebyshev coefficients is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Chebyshev coefficients are the basis of polynomial approximations of functions. Write a program to generate Chebyshev coefficients.

Calculate coefficients: cosine function, 10 coefficients, interval 0 1

C

<lang C> // Program to calculate Chebyshev coefficients // Code taken from Numerical Recipes in C 1/e

1. include <math.h>
2. define PI 3.141592653589793

void chebft(float a, float b, float c[], int n, float (*func)()) {

     int k,j;
     float fac,bpa,bma,f[300];

     bma = 0.5 * (b-a)
     bpa = 0.5 * (b+a)
     for(k = 0;k<n;k++) {
           float y = cos(PI*(k+0.5)/n);
           f[k] = (*func)(y*bma+bpa);
     }
     fac = 2.0/n;
     for (j = 0;j<n;j++) {
           double sum = 0.0;
           for(k = 0;k<n;k++)
                 sum += f[k] * cos(PI*j*(k+0.5)/n);
           c[j] = fac*sum;
     }

} </lang>

J

From 'J for C Programmers: Calculating Chebyshev Coefficients [[1]] <lang J> chebft =: adverb define

f =. u 0.5 * (+/y) - (-/y) * 2 o. o. (0.5 + i. x) % x

  (2 % x) * +/ f * 2 o. o. (0.5 + i. x) *"0 1 (i. x) % x

) </lang> Calculate coefficients: <lang J>

     10 (2&o.) chebft 0 1

1.64717 _0.232299 _0.0537151 0.00245824 0.000282119 _7.72223e_6 _5.89856e_7 1.15214e_8 6.59629e_10 _1.00227e_11 </lang>