The Chebyshev solution of the linear matrix equation \(AX+YB=C\)
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.
scientific article; zbMATH DE number 3888804
scientific article