Abstract
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. Algorithms for the construction of the orthogonal polynomials for the new weight v in terms of those for the old weight w are presented. All the methods are based on modified moments. As applications we present Gaussian quadrature rules for integrals in which the integrant has singularities close to the interval of integration, and the generation of orthogonal polynomials for the (finite) Hermite weight e-t2, supported on a finite interval [-b, b].
| Original language | English |
|---|---|
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 43 |
| Issue number | 1-2 |
| Pages (from-to) | 99-115 |
| Number of pages | 17 |
| ISSN | 0377-0427 |
| DOIs | |
| Publication status | Published - 25.11.1992 |
Funding
Corrcsporhxx-to: Dr. B. Fischer, Institute of Applied h&hcmatics, University of Hamburg. W-2000 Hambtirg 13, Germany. * This author’s rcscarch was in part supported by the US Army under grant DAAI, 03-9L-G-0105. Part of this work was done while the first author was visiting the Departmento f Computer Science at the Stanford University. He would like to thank Gene Golub for his hospitality.