Computer Physics Communications Program Library

Programs in Physics & Physical Chemistry

PROGRAM SUMMARY

Manuscript Title: Gaussian quadrature rule for arbitrary weight function and interval
Authors: H. Fukuda, M. Katuya, E. O. Alt, A. V. Matveenko
Program title: AWGQ
Catalogue identifier: ADVB
Journal reference: Comput. Phys. Commun. 167(2005)143
Programming language: Mathematica 4.0.
Computer: Pentium IV 1.7GHz processor.
Operating system: Windows XP.
Keywords: Gaussian quadrature, multidimensional integration, abscissas, weights, symbolic computation.
PACS: 02.60.Jh.
Classification: 4.11.
Nature of problem: Integration of functions.
Solution method: The recurrence relations defining the orthogonal polynomials for arbitrary weight function and integration interval are written in matrix form. The abscissas and weights for the corresponding Gaussian quadrature are found from the solution of the eigenvalue equation for the tridiagonal symmetric Jacobi matrix.
Restrictions: The program is applicable if the moments of the weight function can be evaluated analytically in Mathematica. For our test example the degree of the Gaussian quadrature cannot not be larger than 96.
Running time: The running time of the test run is about 1 [sec] with a Pentium IV 1.7GHz processor.
References:
[1]	William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computing, (Cambridge University Press; 1992).