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SOR-like methods for solving the Sylvester equation

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Author(s): Jakub Kierzkowski

Publication date: July 2 2015

Journal: ScienceOpen Posters

Publisher: ScienceOpen

Conference name: Numerical Algebra, Matrix Theory, Differential-Algebraic Equations, and Control Theory

Keywords: Sylvester equation, SOR-like iterative method, Iterative methods

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Abstract

We present the SOR-like methods and highlight some of their known properties. We give the SOR-like method as proposed by Z. Wo źnicki and propose two similar methods based upon it. All three are stationary iterative methods for solving the Sylvester equation (AX-XB=C). We form two sufficient conditions under which one of those methods will converge. In addition, we present a modification method, based on the following fact: if X is a solution of AX-XB=C, it is also a solution of (A-αIm)X-X(B-αIn)=C. We also present numerical experiments to illustrate the theoretical results and some properties of the methods.

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Conference

Title: ScienceOpen Posters

Publisher: ScienceOpen

Publication date: July 2 2015

Author information

Jakub Kierzkowski https://orcid.org/0000-0002-0623-7696

Article

DOI: 10.14293/P2199-8442.1.SOP-MATH.PCH3PW.v1

SO-VID: bdfd9f84-a7b0-4a31-bb21-3188b0ef0af1

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