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=120 has been determined by the routine dig_laglogmm(100,-1/2,112,4,32). 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/R79P2ZMR for a method based on ordinary moments. Both methods produce the same answers, but the current one takes more than twice as long 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/R7SQ8XDM
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Notes
The dataset consists of one text file and five Matlab scripts.