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32-digit values of the first 100 recurrence coefficients for the second-order cardinal B-spline weight function obtained by discretization

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By Walter Gautschi

Purdue University

32-digit values of the first 100 recurrence coefficients for the weight function w(x)=phi_m(x) on [0,m], m=2

Version 1.0 - published on 01 Dec 2016 doi:10.4231/R74B2Z9Q - cite this Archived on 02 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)=phi_m(x) on [0,m], m=2, are computed by a multicomponent discretization procedure using the routine sr_cBspline_dis(dig,32,100,2) called with the commands 'global dig; dig=34', where dig=34 has been determined by the routine dig_Bspline_dis(100,2,32,2,32), attesting to the high stability of the multicomponent discretization procedure. The results are in complete agreement with those produced by sr_cBspline_cheb.m (cf. doi:10.4231/R7 . . . ), but are obtained ten times as fast. For details concerning the discretization, see Section 3 in Walter Gautschi, "Polynomials orthogonal with respect to cardinal B-spline weight functions", Numerical Algorithms, submitted. The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for arbitrary order m and for different precisions.

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

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