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Iterative solutions to matrix equations of the form \(A_{i}XB_{i}=F_{i}\). (English) Zbl 1197.15009
Summary: This paper is concerned with the numerical solutions to the linear matrix equations \(A_{1}XB_{1}=F_{1}\) and \(A_{2}XB_{2}=F_{2}\); two iterative algorithms are presented to obtain the solutions. For any initial value, it is proved that the iterative solutions obtained by the proposed algorithms converge to their true values. Finally, simulation examples are given to verify the proposed convergence theorems.

MSC:
15A24 Matrix equations and identities
65F30 Other matrix algorithms (MSC2010)
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