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SOR-like methods for solving the Sylvester equation

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Iterative methods, SOR-like iterative method, Sylvester equation

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      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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