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2008•Numerical Linear Algebra with ApplicationsRequires access

Low rank solution of data‐sparse Sylvester equations

Ulrike Baur

Open publisher page 32 citations

Abstract

Abstract In this paper, a method for solving large‐scale Sylvester equations is presented. The method is based on the sign function iteration and is particularly effective for Sylvester equations with factorized right‐hand side. In this case, the solution will be computed in factored form as it is for instance required in model reduction. The hierarchical matrix format and the corresponding formatted arithmetic are integrated in the iteration scheme to make the method feasible for large‐scale computations. Copyright © 2008 John Wiley & Sons, Ltd.

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What this paper is about

Abstract In this paper, a method for solving large‐scale Sylvester equations is presented. The method is based on the sign function iteration and is particularly effective for Sylvester equations with factorized right‐hand side. In this case, the solution will be computed in factored form as it is for instance required in model reduction. The hierarchical matrix format and the corresponding formatted arithmetic are integrated in the iteration scheme to make the method feasible for large‐scale computations. Copyright © 2008 John Wiley & Sons, Ltd.

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Available abstract

Abstract In this paper, a method for solving large‐scale Sylvester equations is presented. The method is based on the sign function iteration and is particularly effective for Sylvester equations with factorized right‐hand side. In this case, the solution will be computed in factored form as it is for instance required in model reduction. The hierarchical matrix format and the corresponding formatted arithmetic are integrated in the iteration scheme to make the method feasible for large‐scale computations. Copyright © 2008 John Wiley & Sons, Ltd.

Key concepts: Sylvester equation, Sylvester's law of inertia, Sylvester matrix, Mathematics, Computation, Rank (graph theory), Sign (mathematics), Matrix (chemical analysis)

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