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2013 An Iterative Method for the Least-Squares Problems of a General Matrix Equation Subjects to Submatrix Constraints
Li-fang Dai, Mao-lin Liang, Yong-hong Shen
J. Appl. Math. 2013: 1-11 (2013). DOI: 10.1155/2013/697947

Abstract

An iterative algorithm is proposed for solving the least-squares problem of a general matrix equation i=1tMiZiNi=F, where Zi (i=1,2,,t) are to be determined centro-symmetric matrices with given central principal submatrices. For any initial iterative matrices, we show that the least-squares solution can be derived by this method within finite iteration steps in the absence of roundoff errors. Meanwhile, the unique optimal approximation solution pair for given matrices Z~i can also be obtained by the least-norm least-squares solution of matrix equation i=1tMiZ-iNi=F-, in which Z-i=Zi-Z~i, F-=F-i=1tMiZ~iNi. The given numerical examples illustrate the efficiency of this algorithm.

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Li-fang Dai. Mao-lin Liang. Yong-hong Shen. "An Iterative Method for the Least-Squares Problems of a General Matrix Equation Subjects to Submatrix Constraints." J. Appl. Math. 2013 1 - 11, 2013. https://doi.org/10.1155/2013/697947

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 06950826
MathSciNet: MR3131002
Digital Object Identifier: 10.1155/2013/697947

Rights: Copyright © 2013 Hindawi

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