| #include <stdio.h> |
| #include <gsl/gsl_math.h> |
| #include <gsl/gsl_sum.h> |
| |
| #define N 20 |
| |
| int |
| main (void) |
| { |
| double t[N]; |
| double sum_accel, err; |
| double sum = 0; |
| int n; |
| |
| gsl_sum_levin_u_workspace * w |
| = gsl_sum_levin_u_alloc (N); |
| |
| const double zeta_2 = M_PI * M_PI / 6.0; |
| |
| /* terms for zeta(2) = \sum_{n=1}^{\infty} 1/n^2 */ |
| |
| for (n = 0; n < N; n++) |
| { |
| double np1 = n + 1.0; |
| t[n] = 1.0 / (np1 * np1); |
| sum += t[n]; |
| } |
| |
| gsl_sum_levin_u_accel (t, N, w, &sum_accel, &err); |
| |
| printf ("term-by-term sum = % .16f using %d terms\n", |
| sum, N); |
| |
| printf ("term-by-term sum = % .16f using %d terms\n", |
| w->sum_plain, w->terms_used); |
| |
| printf ("exact value = % .16f\n", zeta_2); |
| printf ("accelerated sum = % .16f using %d terms\n", |
| sum_accel, w->terms_used); |
| |
| printf ("estimated error = % .16f\n", err); |
| printf ("actual error = % .16f\n", |
| sum_accel - zeta_2); |
| |
| gsl_sum_levin_u_free (w); |
| return 0; |
| } |