On Least Squares Solutions of an Inconsistent Singular Equation AX + XB = C

Some suggestions are made for the computation of "least squares solutions" of AX + XB = C for the case where the square matrices A and -BThave a common eigenvalue and the equation is inconsistent. The method for finding least squares solutions of the inconsistent equation relies on replaci...

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Bibliographic Details
Published in:SIAM journal on applied mathematics 1976-07, Vol.31 (1), p.84-88
Main Authors: Lovass-Nagy, V., Powers, D. L.
Format: Article
Language:English
Subjects:
Algorithms
Coefficients
Eigenvalues
Least squares
Matrices
Matrix equations
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Summary:Some suggestions are made for the computation of "least squares solutions" of AX + XB = C for the case where the square matrices A and -BThave a common eigenvalue and the equation is inconsistent. The method for finding least squares solutions of the inconsistent equation relies on replacing the right-hand side by another matrix G such that the equation AX + XB = G is consistent and any solution of it is a least squares solution of the original equation. The minimum norm least squares solution may be obtained with no essential complication. Most of the matrices to be manipulated are of the size of A or B.
ISSN:0036-1399
1095-712X
DOI:10.1137/0131008