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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Calculation of Gauss quadrature rules

Authors: Gene H. Golub and John H. Welsch
Journal: Math. Comp. 23 (1969), 221-230
MathSciNet review: 0245201
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Abstract: Several algorithms are given and compared for computing Gauss quadrature rules. It is shown that given the three term recurrence relation for the orthogonal polynomials generated by the weight function, the quadrature rule may be generated by computing the eigenvalues and first component of the orthornormalized eigenvectors of a symmetric tridiagonal matrix. An algorithm is also presented for computing the three term recurrence relation from the moments of the weight function.

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Article copyright: © Copyright 1969 American Mathematical Society