269
Views
11
CrossRef citations to date
0
Altmetric
Section B

Iterative methods for solving linear matrix equation and linear matrix system

&
Pages 763-774 | Received 11 May 2007, Accepted 19 Apr 2008, Published online: 19 Dec 2008
 

Abstract

In this paper, an efficient iterative method is presented to solve the linear matrix equation (X) = E with real matrix X. By this iterative method, the solvability of the linear matrix equation can be determined automatically. When the matrix equation is consistent, then, for any initial matrix X 0, a solution can be obtained within finite iteration steps in the absence of roundoff errors, and the least norm solution can be obtained by choosing a special kind of initial matrix. We also propose an iterative algorithm to obtain the solution or the least norm solution of the consistent matrix system. The given numerical examples demonstrate the efficiency of these two algorithms.

Acknowledgements

The authors are very much indebted to the valuable comments and helpful suggestions of the two referees. The research of this paper was supported by the Science and Technology Commission of Shanghai Municipality through Grant (No. 04JC14031), the China Postdoctoral Science Foundation (No. 20060400634) and the Shanghai Priority Academic Discipline Foundation.

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.