Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 233, Issue 4, Pages 1035-1045Publisher
ELSEVIER
DOI: 10.1016/j.cam.2009.08.108
Keywords
Sylvester equation; Factored ADI method; Galerkin projection
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Funding
- National Science Foundation [DMS-0510664, DMS-0702335, 235-2352818-1042]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [810506] Funding Source: National Science Foundation
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This paper is concerned with the numerical solution of large scale Sylvester equations AX - XB = C, Lyapunov equations as a special case in particular included, with C having very small rank. For stable Lyapunov equations, Penzi (2000) [22] and Li and White (2002) [20] demonstrated that the so-called Cholesky factor ADI method with decent shift parameters can be very effective. in this paper we present a generalization of the Cholesky factor ADI method for Sylvester equations. An easily implementable extension of Penz's shift strategy for the Lyapunov equation is presented for the current case. It Is demonstrated that Galerkin projection via ADI subspaces often produces much more accurate solutions than ADI solutions. (C) 2009 Elsevier B.V. All rights reserved.
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