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.
• Other Names: Chu Eric guestEditor.; Lin Wen‐wei guestEditor.; Reichel Lothar guestEditor.
• 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: ADI preconditioner -- block Arnoldi -- Stein -- Sylvester equation; Algebras, Linear -- Periodicals; 512.5
• DOI: 10.1002/nla.831
• Languages: English
• ISSNs: 1070-5325

Abstract

SUMMARY: In this paper, we propose a block Arnoldi method for solving the continuous low‐rank Sylvester matrix equation AX + XB = EF T . We consider the case where both A and B are large and sparse real matrices, and E and F 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 & Sons, Ltd.