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 GNU Scientific Library Reference Manual - Third Edition (v1.12) by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. RossiPaperback (6"x9"), 592 pages, 60 figuresISBN 0954612078RRP £24.95 (\$39.95)

# 23 Monte Carlo Integration

This chapter describes routines for multidimensional Monte Carlo integration. These include the traditional Monte Carlo method and adaptive algorithms such as vegas and miser which use importance sampling and stratified sampling techniques. Each algorithm computes an estimate of a multidimensional definite integral of the form,

I = \int_xl^xu dx \int_yl^yu  dy ...  f(x, y, ...)


over a hypercubic region ((x_l,x_u), (y_l,y_u), ...) using a fixed number of function calls. The routines also provide a statistical estimate of the error on the result. This error estimate should be taken as a guide rather than as a strict error bound--random sampling of the region may not uncover all the important features of the function, resulting in an underestimate of the error.

The functions are defined in separate header files for each routine, ‘gsl_monte_plain.h’, ‘gsl_monte_miser.h’ and ‘gsl_monte_vegas.h’.

 ISBN 0954612078 GNU Scientific Library Reference Manual - Third Edition (v1.12) See the print edition