32-digit values of the first 100 recurrence coefficients for the symmetric Laguerre weight function

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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(-|x|) on [-Inf,Inf]

Version 1.0 - published on 14 Feb 2017 doi:10.4231/R7QF8QVK - cite this Archived on 15 Mar 2017

Licensed under Attribution 3.0 Unported

Description

32-digit values of the first 100 recurrence coefficients for the weight function w(x)=exp(-|x|) on [-Inf,Inf] are computed by a 2-component discretization procedure. In theory, the procedure yields exact answers after just one iteration in the routine smcdis.m (that is, kount=1). Errors in machine arithmetic, however, may prevent this from happening. Therefore, an extra command is inserted in the routine smcdis.m hat halts it as soon as kount becomes larger than 1. The routine dig_slagsymm(100,dig0,2,32) then determines the smallest number dig0 that does not cause a halt. (Try, for example, dig0=68, which will cause a halt; dig0=70 will not.) Thereafter, the routine [ab,Mcap,kount]=sr_lagsymm(nofdig,N), with nofdig=32, N=100, and dig=72 entered when prompted, yields the desired array ab of recurrence coefficients, along with the (expected) number kount=1 of iterations and the number Mcap of quadrature points needed in the routine smcdis.m.

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

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