6533b85bfe1ef96bd12ba893

RESEARCH PRODUCT

Gaussian quadrature rule for arbitrary weight function and interval

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Abstract A program for calculating abscissas and weights of Gaussian quadrature rules for arbitrary weight functions and intervals is reported. The program is written in Mathematica. The only requirement is that the moments of the weight function can be evaluated analytically in Mathematica. The result is a FORTRAN subroutine ready to be utilized for quadrature. Program summary Title of program: AWGQ Catalogue identifier:ADVB Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADVB Program obtained from: CPC Program Library, Queens University, Belfast, N. Ireland Computer for which the program is designed and others on which it has been tested: Computers: Pentium IV 1.7 GHz processor Installations: 512 MB RAM Operating systems or monitors under which the program has been tested: Windows XP Programming language used: Mathematica 4.0 No. of processors used: 1 Has the code been vectorized or parallelized?: No No. of lines in distributed program, including test data, etc.:1076 No. of bytes in distributed program, including test data, etc.: 32 681 Operating systems under which program has been tested: FORTRAN Distribution format: tar.gz Nature of physical problem: Integration of functions. Method of solution: 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 on the complexity of the problem: 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. Typical running time: The running time of the test run is about 1 [s] with a Pentium IV 1.7 GHz processor.