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An iterative method for the bisymmetric solutions of the consistent matrix equations \(A_{1}XB_{1}=C_{1}, A_{2}XB_{2}=C_{2}\). (English) Zbl 1202.65052

Summary: An iterative method is presented for finding the bisymmetric solutions of a pair of consistent matrix equations \(A_{1}XB_{1}=C_{1}, A_{2}XB_{2}=C_{2}\), by which a bisymmetric solution can be obtained in finite iteration steps in the absence of round-off errors. Moreover, the solution with least Frobenius norm can be obtained by choosing a special kind of initial matrix. In the solution set of the matrix equations, the optimal approximation bisymmetric solution to a given matrix can also be derived by this iterative method. The efficiency of the proposed algorithm is shown by some numerical examples.

MSC:

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

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