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

KELLEY
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References:

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