RMOP: Repeated modifications of orthogonal polynomials

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By Walter Gautschi

Purdue University

Matlab routines and data sets that compute repeated modifications of orthogonal polynomials

Version 1.0 - published on 23 Apr 2014 doi:10.4231/R7F18WNB - cite this Archived on 25 Oct 2016

Licensed under CC0 1.0 Universal

Description

Algorithms are developed for computing the coefficients in the three-term recurrence relation of repeatedly modified orthogonal polynomials, the modifications involving division of the orthogonality measure by a linear function with real or complex coefficient. The respective Gaussian quadrature rules can be used to account for simple or multiple poles that may be present in the integrand. Several examples are given to illustrate this.

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This dataset contains 20 Matlab codes and 2 data sets:

Matlab:

  • schri4.m
  • rschri4.m
  • mod_md.m
  • rho0.m
  • sr_jacobi.m
  • sr_jacobi01.m
  • gauss.m
  • Example1.m
  • f1.m
  • test_precision1.m
  • Example2.m
  • f2.m
  • sr_laguerre.m
  • test_precision3.m
  • Example3.m
  • f3.m
  • einstein.m
  • Example4.m
  • mod_d.m
  • Example5.m
  • f5.m

Data sets:

  • beps1
  • abeps2

This is a companion piece to the paper "Repeated modifications of orthogonal polynomials by linear divisors", Numerical Algorithms, 2013, Volume 63, Issue 2, pp. 369-383. doi: 10.1007/s11075-012-9627-1.

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