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Numerical Algorithms

, Volume 6, Issue 2, pp 205–227 | Cite as

Jacobi matrices for measures modified by a rational factor

  • Sylvan Elhay
  • Jaroslav Kautsky
Article

Abstract

This paper describes how, given the Jacobi matrixJ for the measure dσ(t), it is possible to produce the Jacobi matrix Ĵ for the measurer(t)dσ(t) wherer(t) is a quotient of polynomials. The method uses a new factoring algorithm to generate the Jacobi matrices associated with the partial fraction decomposition ofr(t) and then applies a previously developed summing technique to merge these Jacobi matrices. The factoring method performs best just where Gautschi's minimal solution method for this problem is weakest and vice versa. This suggests a hybrid strategy which is believed to be the most powerful yet for solving this problem. The method is demonstrated on a simple example and some numerical tests illustrate its performance characteristics.

Keywords

Orthogonal polynomials Jacobi matrices rational factors modifying measures Gauss quadratures 

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Copyright information

© J.C. Baltzer AG, Science Publishers 1994

Authors and Affiliations

  • Sylvan Elhay
    • 1
  • Jaroslav Kautsky
    • 2
  1. 1.Computer Science DepartmentUniversity of AdelaideSouth AustraliaAustralia
  2. 2.School of Information Science and TechnologyFlinders UniversityBedford ParkAustralia

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