How to generate unknown orthogonal polynomials out of known orthogonal polynomials
نویسنده
چکیده
We consider the problem of generating the three-term recursion coefficients of orthogonal polynomials for a weight function v(t) = r(t)w(t), obtained by modifying a given weight function w by a rational function r. Algorithms for the construction of the orthogonal polynomials for the new weight v in terms of those for the old weight w axe presented. All the methods are based on modified moments. As applications we present Gaussian quadrature rules for integrals in which the integrand has singularities close to the interval of integration, and the generation of orthogonal polynomials for the (finite) Hermite weight eet2, supported on a finite interval [-b, b]. 1980 Mathematics Subject Classification. Primary 65F25; Secondary 33A65. The second author was in part supported by the US Army under grant DAAL 03-90-G-0105. 2 Bernd Fischer and Gene H. Golub
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