LSQR iterative method for generalized coupled Sylvester matrix equations

An iterative method is proposed to solve generalized coupled Sylvester matrix equations, based on a matrix form of the least-squares QR-factorization (LSQR) algorithm. By this iterative method on the selection of special initial matrices, we can obtain the minimum Frobenius norm solutions or the min...

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Veröffentlicht in:Applied mathematical modelling Jg. 36; H. 8; S. 3545 - 3554
Hauptverfasser: Li, Sheng-Kun, Huang, Ting-Zhu
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.08.2012
Schlagworte:
Approximation
Generalized coupled Sylvester matrix equations
Iterative methods
Least squares method
LSQR algorithm
Mathematical analysis
Mathematical models
Matrices
Matrix methods
Minimum Frobenius norm solutions
Norms
Generalized coupled Sylvester matrix equations
Minimum Frobenius norm solutions
LSQR algorithm
ISSN:0307-904X
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Zusammenfassung:An iterative method is proposed to solve generalized coupled Sylvester matrix equations, based on a matrix form of the least-squares QR-factorization (LSQR) algorithm. By this iterative method on the selection of special initial matrices, we can obtain the minimum Frobenius norm solutions or the minimum Frobenius norm least-squares solutions over some constrained matrices, such as symmetric, generalized bisymmetric and (R,S)-symmetric matrices. Meanwhile, the optimal approximate solutions to the given matrices can be derived by solving the corresponding new generalized coupled Sylvester matrix equations. Finally, numerical examples are given to illustrate the effectiveness of the present method.
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ISSN:0307-904X
DOI:10.1016/j.apm.2011.10.030