Calculation of Gauss quadrature rules

1969/01/01 by Gene H. Golub, John H. Welsch · 36 citations
Physics and Astronomy · Computer Science · #Scientific Research and Discoveries #Matrix Theory and Algorithms

paper · doi:10.1090/s0025-5718-69-99647-1

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.

Citations

• The QR Transformation A Unitary Analogue to the LR Transformation--Part 1

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