32-digit values of the first 100 recurrence coefficients, obtained from moments, for a radiative transfer weight function with parameter c=2/3

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By Walter Gautschi

Purdue University

32-digit values of the first 100 recurrence coefficients for the weight function w(x)=exp(-1/x) on [0,c], c=2/3

Version 1.0 - published on 08 Dec 2016 doi:10.4231/R7N014H9 - cite this Archived on 09 Jan 2017

Licensed under Attribution 3.0 Unported

Description

32-digit values of the first 100 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=exp(-1/x) on [0,c], c=2/3, are computed by a moment-based method using the routine sr_radtrans_cheb(dig,32,100,2/3), where dig=194 has been determined by the routine dig_radtrans_cheb(100,2/3,186,4,32). The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for an arbitrary parameter c > 0 as well as for different precisions. The polynomials here obtained are closely related to the radiative transfer polynomials in Section 4 of Martin J. Gander and Alan H. Karp, "Stable computation of high order Gauss quadrature rules using discretization for measures in radiation transfer", Journal of Quantitative Spectroscopy & Radiative Transfer" 68 (2001), 213-223. The alpha-coefficients of the latter, as well as the first beta-coefficient, are obtained by dividing ours by c, and the remaining beta-coefficients by dividing ours by c^2. The results are in complete agreement with those produced by sr_radtrans_dis.m (cf. doi:10.4231/R7CF9N35) but are obtained about six times faster.

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The dataset consists of one text file and five Matlab scripts.

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