32-digit values of the first 100 recurrence coefficients for a weight function with a logarithmic type singularity

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By Walter Gautschi

Purdue University

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

Version 1.0 - published on 22 Mar 2017 doi:10.4231/R7BR8Q6R - cite this Archived on 23 Apr 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)=-log(1-x^2) on [-1,1] are computed by a modified-moment-based method using the routine sr_logtype(dig,32,100), where dig=36 has been determined by the routine dig_logtype(100,34,2,32), attesting to the high stability of the modified Chebyshev algorithm. For relevant computational details see Dirk P. Laurie and Laurette Rolfes, "Computation of Gaussian quadrature rules from modified moments --- Algorithm 015", J. Comput. Apppl. Math. 5 (1979), 235-243. (The 25-digit values of the Gauss nodes and weights in the table on p. 237 of the cited reference, however, seem to be accurate to only about 15-16 digits, judging from comparison with results obtained with our own recurrence coefficients and also from the fact that for the 5-point published Gauss formula, the sum of the weights reproduces the first moment only to about 16 digits, whereas with our data, for 5-, 10-, 20-, 30-point formulae we obtain agreement to all 32 digits.)

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

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