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The submatrix constraint problem of matrix equation \(AXB+CYD=E\). (English) Zbl 1189.65079

This paper deals with the real matrix equation \(AXB+CYD=E\), where \(X\) of order \(n\) is symmetric centrosymmetric \(-\) that is: \(x_{ij}=x_{ji}=x_{n-j+1,n-i+1}\), and \(Y\) of order \(m\) is symmetric. It is presented an algorithm to minimize the \(\| AXB+CYD-E\|\) in the Frobenious norm, using the conjugate gradient square method. Then, a second algorithm for the optimal approximation of the solution set is derived. Also the stability of the algorithms and numerical behaviors are studied.

MSC:

65F30 Other matrix algorithms (MSC2010)
15A24 Matrix equations and identities

Software:

KELLEY
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References:

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