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Variable-precision recurrence coefficients for nonstandard orthogonal polynomials

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Abstract

A symbolic/variable-precision procedure is described (and implemented in Matlab) that generates an arbitrary number N of recurrence coefficients for orthogonal polynomials to any given precision nofdig. The only requirement is the availability of a variable-precision routine for computing the first 2 N moments of the underlying weight function to any precision dig > nofdig. The procedure is applied to Freud, Bose–Einstein, and Fermi–Dirac orthogonal polynomials.

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Authors and Affiliations

  1. Department of Computer Sciences, Purdue University, West Lafayette, IN, 47907-2066, USA

    Walter Gautschi

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  1. Walter Gautschi
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Correspondence to Walter Gautschi.

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Gautschi, W. Variable-precision recurrence coefficients for nonstandard orthogonal polynomials. Numer Algor 52, 409–418 (2009). https://doi.org/10.1007/s11075-009-9283-2

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  • DOI: https://doi.org/10.1007/s11075-009-9283-2

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