BIT Numerical Mathematics

, Volume 33, Issue 3, pp 473–484

Fast inversion of vandermonde-like matrices involving orthogonal polynomials

  • D. Calvetti
  • L. Reichel
Part II Numerical Mathematics

DOI: 10.1007/BF01990529

Cite this article as:
Calvetti, D. & Reichel, L. BIT (1993) 33: 473. doi:10.1007/BF01990529

Abstract

Let {q}j=0n−1 be a family of polynomials that satisfy a three-term recurrence relation and let {tk}k=1n be a set of distinct nodes. Define the Vandermonde-like matrixWn=[wjk]k,j=1n,wjk=qj−1(tk). We describe a fast algorithm for computing the elements of the inverse ofWn inO(n2) arithmetic operations. Our algorithm generalizes a scheme presented by Traub [22] for fast inversion of Vandermonde matrices. Numerical examples show that our scheme often yields higher accuracy than the LINPACK subroutine SGEDI for inverting a general matrix. SGEDI uses Gaussian elimination with partial pivoting and requiresO(n3) arithmetic operations.

AMS(MOS) Subject classification

65F0565D0565D30

Key words

Vandermonde matrixinversefast algorithmLeja ordering

Copyright information

© the BIT Foundation 1993

Authors and Affiliations

  • D. Calvetti
    • 1
  • L. Reichel
    • 2
  1. 1.Department of Pure and Applied MathematicsStevens Institute of TechnologyHoboken
  2. 2.Department of Mathematics and Computer ScienceKent State UniversityKent