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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.

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