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Numerical DifferentiationThe functions described in this chapter compute numerical derivatives by finite differencing. An adaptive algorithm is used to find the best choice of finite difference and to estimate the error in the derivative. These functions are declared in the header file `gsl_diff.h' Functions
Example
The following code estimates the derivative of the function
f(x) = x^{3/2}
at x=2 and at x=0. The function f(x) is
undefined for x<0 so the derivative at x=0 is computed
using #include <stdio.h> #include <gsl/gsl_math.h> #include <gsl/gsl_diff.h> double f (double x, void * params) { return pow (x, 1.5); } int main (void) { gsl_function F; double result, abserr; F.function = &f; F.params = 0; printf("f(x) = x^(3/2)\n"); gsl_diff_central (&F, 2.0, &result, &abserr); printf("x = 2.0\n"); printf("f'(x) = %.10f +/ %.5f\n", result, abserr); printf("exact = %.10f\n\n", 1.5 * sqrt(2.0)); gsl_diff_forward (&F, 0.0, &result, &abserr); printf("x = 0.0\n"); printf("f'(x) = %.10f +/ %.5f\n", result, abserr); printf("exact = %.10f\n", 0.0); return 0; } Here is the output of the program, $ ./demo f(x) = x^(3/2) x = 2.0 f'(x) = 2.1213203435 +/ 0.01490 exact = 2.1213203436 x = 0.0 f'(x) = 0.0012172897 +/ 0.05028 exact = 0.0000000000 References and Further ReadingThe algorithms used by these functions are described in the following book,
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