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Least squares solution of $$BXA^T=T$$ over symmetric, skew-symmetric, and positive semidefinite $$X$$. (English) Zbl 1050.65037
The paper is devoted to a class of Procrustes problems, where the solution is required to be skew-symmetric, or positive semidefinite (maybe asymmetrical). An efficient method is used to solve the constrained least square problem over and positive semidefinite matrix $$X$$. The proposed solution is based on the QSVD factorization of the given matrix pair $$[A,B]$$, which is used to reduce the problem to one with a given diagonal matrix. The general expression of the solution is given and some necessary and sufficient conditions are derived about the solvability of the matrix equation $$BXA'=T$$. In each case an algorithm is given for the unique solution when $$B$$ and $$A$$ are of full column rank.

##### MSC:
 65F20 Numerical solutions to overdetermined systems, pseudoinverses 65G30 Interval and finite arithmetic 15A24 Matrix equations and identities
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