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Least-square solutions for inverse problems of centrosymmetric matrices. (English) Zbl 1050.65040

The authors aim at computing a centrosymmetric matrix \(A\) which solves the linear least-squares problem \(\min \| AX-B\| _2\) for given matrices \(X\) and \(B\). Moreover, the problem of finding the nearest matrix from a certain subset of centrosymmetric matrices to a general matrix is considered. All obtained formulas and algorithms are based on the well-known fact that a simple orthogonal similarity transformation can be used to transform any centrosymmetric matrix into a block diagonal matrix with two non-structured diagonal blocks. This admits the use of standard methods for solving the subproblems associated with these diagonal blocks, which in turn yields the solution to the original problem.

MSC:

65F20 Numerical solutions to overdetermined systems, pseudoinverses
15A29 Inverse problems in linear algebra
15B57 Hermitian, skew-Hermitian, and related matrices
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