A preconditioned block Arnoldi method for large Sylvester matrix equations. Issue 2 (7th December 2011)

• Record Type: Journal Article
• Authors: Bouhamidi, A.; Hached, M.; Heyouni, M.; Jbilou, K.; Chu, Eric; Lin, Wen‐wei; Reichel, Lothar
• Is Part Of: Numerical linear algebra with applications. Volume 20:Issue 2(2013:Mar.)
• Page Start: 208
• Page End: 219
• Publication Date: 2011-12-07
• Subjects: Algebras, Linear -- Periodicals; 512.5
• DOI: 10.1002/nla.831
• Languages: English
• ISSNs: 1070-5325

Abstract

<abstract abstract-type="main" id="nla831-abs-0001"> <title>SUMMARY</title> <p id="nla831-para-0001">In this paper, we propose a block Arnoldi method for solving the continuous low‐rank Sylvester matrix equation <italic>AX</italic> + <italic>XB</italic> = <italic>EF</italic>^{<italic>T</italic>}. We consider the case where both <italic>A</italic> and <italic>B</italic> are large and sparse real matrices, and <italic>E</italic> and <italic>F</italic> are real matrices with small rank. We first apply an alternating directional implicit preconditioner to our equation, turning it into a Stein matrix equation. We then apply a block Krylov method to the Stein equation to extract low‐rank approximate solutions. We give some theoretical results and report numerical experiments to show the efficiency of this method. Copyright © 2011 John Wiley &amp; Sons, Ltd.</p> </abstract>