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A preconditioned block Arnoldi method for large Sylvester matrix equations
Author(s) -
Bouhamidi A.,
Hached M.,
Heyouni M.,
Jbilou K.
Publication year - 2013
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.831
Subject(s) - sylvester equation , preconditioner , mathematics , rank (graph theory) , arnoldi iteration , block (permutation group theory) , matrix (chemical analysis) , sylvester matrix , sylvester's law of inertia , krylov subspace , algebra over a field , symmetric matrix , algorithm , iterative method , mathematical analysis , pure mathematics , combinatorics , eigenvalues and eigenvectors , matrix polynomial , chemistry , physics , quantum mechanics , chromatography , polynomial matrix , polynomial
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.
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