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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Bibliographic Details
Published in:Applied mathematical modelling Vol. 36; no. 8; pp. 3545 - 3554
Main Authors: Li, Sheng-Kun, Huang, Ting-Zhu
Format: Journal Article
Language:English
Published: Elsevier Inc 01.08.2012
Subjects:
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
Online Access:Get full text
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Summary: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