Description
32-digit values of the first 100 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=x^a*exp(-x)*(x-1-log(x)) on [0,Inf], a=1/2, are computed by a modified-moment-based method using the routine sr_laglogmm(dig,32,100,1/2), where dig=116 has been determined by the routine dig_laglogmm(100,1/2,108,4,32). For the modified moments, see Section 2.2 in Walter Gautschi, "Gauss quadrature routines for two classes of logarithmic weight functions", Numerical Algorithms 55 (2010), 265-277, doi: 10.1007/s11075-010-9366-0, and Section 1 for an application. The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for arbitrary a > -1 as well as for different precisions. See also doi:10.4231/R7JH3J5S for a method based on ordinary moments. Both methods produce the same answers, but the current one is about 60% faster to run.
Cite this work
Researchers should cite this work as follows:
- Gautschi, W. (2016). 32-digit values of the first 100 recurrence coefficients for the weight function w(x)=x^(1/2)*exp(-x)*(x-1-log(x)) on [0,Inf] obtained from modified moments. Purdue University Research Repository. doi:10.4231/R78P5XHT
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Notes
The dataset consists of one text file and five Matlab scripts.