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Interpolatory integration rules and orthogonal polynomials with varying weights |
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| Authors: | T. Bloom D. S. Lubinsky H. Stahl |
| Affiliation: | (1) Department of Mathematics, University of Toronto, M5S 1A1 Toronto, Ontario, Canada;(2) Department of Mathematics, University of the Witwatersrand, P.O. Wits 2050, Republic of South Africa;(3) Technische Fachhochschule Berlin/FB2, Luxemburgerstr. 10, D-1000 Berlin 65, Germany |
| Abstract: | We investigate which types of asymptotic distributions can be generated by the knots of convergent sequences of interpolatory integration rules. It will turn out that the class of all possible distributions can be described exactly, and it will be shown that the zeros of polynomials that are orthogonal with respect to varying weight functions are good candidates for knots of integration rules with a prescribed asymptotic distribution.Research supported by the Deutsche Forschungsgemeinschaft (AZ: Sta 299/4-2). |
| Keywords: | Interpolatory integration rules convergent integration rules orthogonal polynomials varying weights equilibrium distribution |
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