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Least squares symmetric solutions to a matrix equation with a matrix inequality constraint. (English) Zbl 1307.15020

Summary: In this paper, an iteration method to compute the least squares symmetric solutions of the matrix equation \(AXB=C\) subject to a matrix inequality constraint \(EXF\geq D\) is given. Some convergence results of the algorithm are proved. Numerical experiments are given to illustrate the proposed algorithm can be used to compute the minimum Frobenius norm symmetric solution of the consistent matrix equation \(AXB=C\) the minimum Frobenius norm least squares symmetric solution of the inconsistent matrix equation \(AXB=C\), a symmetric solution of the consistent matrix inequality \(AXB \geq C\), a symmetric solution of the consistent matrix equation \(AXB=C\) under the consistent matrix inequality \(EXF\geq D\) constraint, and the minimum Frobenius norm symmetric solution of the consistent matrix equations \((AXB, EXF)=(C,D)\).

MSC:

15A24 Matrix equations and identities
15A39 Linear inequalities of matrices
65F30 Other matrix algorithms (MSC2010)

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