Calculation of Gauss quadrature rules

Author:

Golub Gene H.,Welsch John H.

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference12 articles.

1. Tables for the evaluation of ∫₀^{∞}𝑥^{𝛽}𝑒^{-𝑥}𝑓(𝑥)𝑑𝑥 by Gauss-Laguerre quadrature;Concus, P.;Math. Comp.,1963

2. D. Corneil, Eigenvalues and Orthogonal Eigenvectors of Real Symmetric Matrices, Institute of Computer Science Report, Univ. of Toronto, 1965.

3. National Bureau of Standards Applied Mathematics Series, No. 55;Abramowitz, Milton,1964

4. The 𝑄𝑅 transformation: a unitary analogue to the 𝐿𝑅 transformation. I;Francis, J. G. F.;Comput. J.,1961

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