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HPGT: High-precision Gauss-Turan quadrature rules

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By Walter Gautschi

Purdue University

Matlab routines that calculate high-precision Gauss-Turan quadrature rules

Version 1.0 - published on 23 Apr 2014 doi:10.4231/R71V5BW8 - cite this Archived on 25 Oct 2016

Licensed under CC0 1.0 Universal

Description

Matlab software are presented for generating Gauss–Turán quadrature rules for the Laguerre and Hermite weight functions to arbitrarily high accuracy. This is accomplished by the Newton–Kantorovich method, using initial approximations that are sufficiently accurate to be capable of producing n-point quadrature formulae for n as large as 42 in the case of the Laguerre weight function, and 90 in the case of the Hermite weight function.

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Notes

This dataset contains 17 Matlab codes and files:

  • sr_laguerre.m
  • sgauss.m
  • sr_hermite.m
  • sturan.m
  • sturan_laguerre.m
  • sturan_hermite.m
  • sturan_laguerre_explore.m
  • sroot.m
  • p.m
  • pd.m
  • linfunGTL.m
  • quadfunGTL.m
  • timingSTL.m
  • runSTL.m
  • sturan_hermite_explore.m
  • linfunGTH.m
  • runSTH.m

These files serve as a companion piece to the paper, "High-precision Gauss-Turan quadrature rules for Laguerre and Hermite weight functions," Numerical Algorithms 67(2014), 59-72.

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