QNG non-adaptive Gauss-Kronrod integration - GNU Scientific Library -- Reference Manual
Description: GNU Scientific Library -- Reference Manual

Next: QAG adaptive integration, Previous: Numerical Integration Introduction, Up: Numerical Integration

### 17.2 QNG non-adaptive Gauss-Kronrod integration

The QNG algorithm is a non-adaptive procedure which uses fixed Gauss-Kronrod-Patterson abscissae to sample the integrand at a maximum of 87 points. It is provided for fast integration of smooth functions.

— Function: int gsl_integration_qng (const gsl_function * f, double a, double b, double epsabs, double epsrel, double * result, double * abserr, size_t * neval)

> This function applies the Gauss-Kronrod 10-point, 21-point, 43-point and 87-point integration rules in succession until an estimate of the integral of f over (a,b) is achieved within the desired absolute and relative error limits, epsabs and epsrel. The function returns the final approximation, result, an estimate of the absolute error, abserr and the number of function evaluations used, neval. The Gauss-Kronrod rules are designed in such a way that each rule uses all the results of its predecessors, in order to minimize the total number of function evaluations.

The GNU Scientific Library - a free numerical library licensed under the GNU GPL
Back to the GNU Scientific Library Homepage