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=10, are computed by a multicomponent discretization procedure using the routine sr_cBspline_dis(34,32,100,10) called by run_cBspline.m. 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 results obtained are in complete agreement with the thirty 20-digit recurrence coefficients given in Section 3 of Gradimir V. Milovanović, "Symbolic-numeric computation of orthogonal polynomials and Gaussian quadratures with respect to the cardinal B-spline", Numerical Algorithms, to appear. The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for arbitrary order m and for different precisions.
Cite this work
Researchers should cite this work as follows:
- Gautschi, W. (2016). 32-digit values of the first 100 recurrence coefficients for the 10th-order cardinal B-spline weight function. Purdue University Research Repository. doi:10.4231/R70K26JX
The dataset consists of one text file and nine Matlab scripts.