37
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

An iterative algorithm for approximate orthogonalisation of symmetric matrices

, &
Pages 215-226 | Received 14 May 2003, Accepted 09 Jun 2003, Published online: 12 May 2010
 

Abstract

In a previous article, one of the authors presented an extension of an iterative approximate orthogonalisation algorithm, due to Z. Kovarik, for arbitrary rectangular matrices. In the present article, we propose a modified version of this extension for the class of arbitrary symmetric matrices. For this new algorithm, the computational effort per iteration is much smaller than for the initial one. We prove its convergence and also derive an error reduction factor per iteration. In the second part of the article, we show that we can eliminate the matrix inversion required by the previous algorithm in each iteration, by replacing it with a polynomial matrix expression. Some numerical experiments are also presented for a collocation discretisation of a first kind integral equation.

*All the computations were made with the Numerical Linear Algebra software package OCTAVE, freely available under the terms of the GNU General Public License, see www.octave.org

Acknowledgments

The article was supported by NATO through collaborative linkage grant PST.CLG.977924 and by the DAAD via a grant that one of the authors had as a visiting professor at the Friedrich-Alexander-Universität Erlangen–Nürnberg, Germany, in the period October 2002–August 2003.

Notes

*All the computations were made with the Numerical Linear Algebra software package OCTAVE, freely available under the terms of the GNU General Public License, see www.octave.org

Log in via your institution

Log in to Taylor & Francis Online

PDF download + Online access

  • 48 hours access to article PDF & online version
  • Article PDF can be downloaded
  • Article PDF can be printed
USD 61.00 Add to cart

Issue Purchase

  • 30 days online access to complete issue
  • Article PDFs can be downloaded
  • Article PDFs can be printed
USD 1,129.00 Add to cart

* Local tax will be added as applicable

Related Research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.