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Least squares solutions to \(AX = B\) for bisymmetric matrices under a central principal submatrix constraint and the optimal approximation. (English) Zbl 1133.15016

A square matrix is bisymmetric if it is symmetric w.r.t. the diagonal and the antidiagonal. The authors consider least squares solutions to the matrix equation \(AX=B\) under a central principal matrix constaint for \(A\) and the optimal approximation. A central principal submatrix is obtained by deleting the same number of rows and columns in the edges. The authors first discuss the structure of bisymmetric matrices and their principal submatrices. Then they give necessary and sufficient conditions for the solvability of the least squares problem, and derive the general representation of the solutions. They express also the solution to the corresponding optimal approximation problem.

MSC:

15A24 Matrix equations and identities
15B57 Hermitian, skew-Hermitian, and related matrices
65F20 Numerical solutions to overdetermined systems, pseudoinverses
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