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The Chebyshev solution of the linear matrix equation $$AX+YB=C$$. (English) Zbl 0557.65024
Properties of the Chebyshev solutions of the linear matrix equation $$AX+YB=C$$ where $$A, B$$ and $$C$$ are given matrices of dimensions $$m\times r$$, $$s\times n$$ and $$m\times n$$, respectively, where $$r<m$$ and $$s<n$$, are investigated. Two particular cases are considered separately. In the first case, $$m=r+1$$ and $$n=s+1,$$ in the second case $$r=s=1$$ and $$m, n$$ are arbitrary. For these two cases, under the assumption that the matrices $$A$$ and $$B$$ are full rank, necessary and sufficient conditions characterizing the Chebyshev solution of $$AX+YB=C$$ and the formulas for the Chebyshev error are formulated. An algorithm, which may be applied to compute the Chebyshev solution of $$AX+YB=C$$ for these particular cases, is proposed. Some numerical examples are also given.
Reviewer: K. Ziętak

##### MSC:
 65F30 Other matrix algorithms (MSC2010) 15A24 Matrix equations and identities
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##### References:
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