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Calculation of Gauss Quadrature Rules

Gene H. Golub and John H. Welsch
Mathematics of Computation
Vol. 23, No. 106 (Apr., 1969), pp. 221-230+s1-s10
DOI: 10.2307/2004418
Stable URL: http://www.jstor.org/stable/2004418
Page Count: 20
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Calculation of Gauss Quadrature Rules
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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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