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

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By Walter Gautschi

Purdue University

32-digit values of the first 100 recurrence coefficients for the weight function w(x)=(1-x)^a*x^b*log(1/x) on [0,1], a = 1/2, b = 1/2

Version 1.0 - published on 22 Nov 2016 doi:10.4231/R76W981N - cite this Archived on 23 Dec 2016

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)=(1-x)^a*x^b*log(1/x) on [0,1], a=1/2, b=1/2, are computed by a modified-moment-based method using the routine sr_jacobilog1(dig,32,100,1/2,1/2), where dig=34 has been determined by the routine dig_jacobilog1(100,1/2,1/2, 32,2,32), attesting to the high stability of the modified Chebyshev algorithm. The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for arbitrary a>-1, b>-1, as well as for different precisions. If the logarithmic singularity occurs at the right endpoint, that is, the logarithmic factor in w(x) is log(1/(1-x)), then the recurrence coefficients are 1-c_k, d_k, where c_k, d_k are the recurrence coefficients for the weight function (1-x)^b*x*a*log(1/x) on [0,1]. For the relevant modified moments, see Section 3.2 of Walter Gautschi, "Gauss quadrature routines for two classes of logarithmic weight functions", Numerical Algorithms 55 (2010), 265-277. doi: doi:10.1007/s11075-010-9366-0.

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

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