The existence and construction of rational Gauss-type quadrature rules
نویسندگان
چکیده
منابع مشابه
The existence and construction of rational Gauss-type quadrature rules
Consider a hermitian positive-definite linear functional F, and assume we have m distinct nodes fixed in advance anywhere on the real line. In this paper we then study the existence and construction of nth rational Gauss-Radau (m = 1) and Gauss-Lobatto (m = 2) quadrature formulas that approximate F{f}. These are quadrature formulas with n positive weights and with the n−m remaining nodes real a...
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When integrating functions that have poles outside the interval of integration, but are regular otherwise, it is suggested that the quadrature rule in question ought to integrate exactly not only polynomials (if any), but also suitable rational functions. The latter are to be chosen so as to match the most important poles of the integrand. We describe two methods for generating such quadrature ...
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The existence of (standard) Gauss quadrature rules with respect to a nonnegative measure dμ with support on the real axis easily can be shown with the aid of orthogonal polynomials with respect to this measure. Efficient algorithms for computing the nodes and weights of an n-point Gauss rule use the n × n symmetric tridiagonal matrix determined by the recursion coefficients for the first n orth...
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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 c...
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Abstract. Gauss quadrature is a popular approach to approximate the value of a desired integral determined by a measure with support on the real axis. Laurie proposed an (n+1)-point quadrature rule that gives an error of the same magnitude and of opposite sign as the associated n-point Gauss quadrature rule for all polynomials of degree up to 2n + 1. This rule is referred to as an anti-Gauss ru...
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ژورنال
عنوان ژورنال: Applied Mathematics and Computation
سال: 2012
ISSN: 0096-3003
DOI: 10.1016/j.amc.2012.04.008