32-digit values of the first 100 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=exp[-(x^{^2}-1)^{^2}/(4*ε)] on [-Inf,Inf], ε=.1, are computed by a multicomponent discretization procedure using the routine sr_OPbimod(32,100) with dig=34, epsi=.1 entered at the prompt. The value dig=34 has been determined by the routine dig_sOPbimod(100,32,2,32), attesting to the high stability of the procedure. (Both routines may take several hours to run.) For details, see Exercise 2.38(c) in Walter Gautschi, "Orthogonal polynomials in MATLAB: Exercises and solutions", SIAM, Philadelphia, PA (2016). Auxiliary routines muOPbimod_gp.m and explore_mu.m are intended to help determine suitable values for the parameter μ needed when ε < 1/10. (This requires a minor temporary change in the routine smcdis.m as explained on p.130 of the cited reference.) The value of μ should be taken to be at least equal to 1; when N = 100, other selected values of μ for ε = .008:-.001:.001 are found to be μ = 1.7, 4.7, 8.0, 15.3, 26.2, 44.4, 84.2, 201.3. The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for arbitrary ε > 0 as well as for different precisions.

Researchers should cite this work as follows:

• Gautschi, W. (2016). 32-digit values of the first 100 recurrence coefficients for the bimodal weight function with parameter ε=.1. Purdue University Research Repository. doi:10.4231/R76T0JNX

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1. Computer Science
2. Computer Science (Dept)
3. Mathematics
4. Modification algorithms for orthogonal polynomials
5. Orthogonal polynomials
6. Walter Gautschi Archives
7. weight functions

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