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.
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Research supported by the Deutsche Forschungsgemeinschaft (AZ: Sta 299/4-2).
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Bloom, T., Lubinsky, D.S. & Stahl, H. Interpolatory integration rules and orthogonal polynomials with varying weights. Numer Algor 3, 55–65 (1992). https://doi.org/10.1007/BF02141915
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DOI: https://doi.org/10.1007/BF02141915