Calculation of Gauss quadrature rules

Authors:
Gene H. Golub and John H. Welsch

Journal:
Math. Comp. **23** (1969), 221-230

DOI:
https://doi.org/10.1090/S0025-5718-69-99647-1

MathSciNet review:
0245201

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Abstract | References | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-69-99647-1

Article copyright:
© Copyright 1969
American Mathematical Society