Asymptotic properties of the QR factorization of banded Hessenberg-Toeplitz matrices

Xiao W. Chang, Martin J. Gander, Samir Karaa

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We consider Givens QR factorization of banded Hessenberg-Toeplitz matrices of large order and relatively small bandwidth. We investigate the asymptotic behaviour of the R factor and Givens rotation when the order of the matrix goes to infinity, and present some interesting convergence properties. These properties can lead to savings in the computation of the exact QR factorization and give insight into the approximate QR factorizations of interest in preconditioning. The properties also reveal the relation between the limit of the main diagonal elements of R and the largest absolute root of a polynomial.

Original languageEnglish
Pages (from-to)659-682
Number of pages24
JournalNumerical Linear Algebra with Applications
Volume12
Issue number7
DOIs
Publication statusPublished - Sep 2005

Fingerprint

Hessenberg Matrix
QR Factorization
Toeplitz matrix
Factorization
Asymptotic Properties
Givens Rotations
Root of a polynomial
Approximate Factorization
Preconditioning
Convergence Properties
Asymptotic Behavior
Bandwidth
Infinity
Polynomials

Keywords

  • Banded Hessenberg-Toeplitz matrices
  • Convergence
  • Discrete and continuous QR factorization

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

Cite this

Asymptotic properties of the QR factorization of banded Hessenberg-Toeplitz matrices. / Chang, Xiao W.; Gander, Martin J.; Karaa, Samir.

In: Numerical Linear Algebra with Applications, Vol. 12, No. 7, 09.2005, p. 659-682.

Research output: Contribution to journalArticle

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