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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 ${\sum }_{i=\mathrm{1}}^{t}\mathrm{‍}{M}_{i}{Z}_{i}{N}_{i}=F$, where ${Z}_{i}$ ($i=\mathrm{1,2},\dots ,t$) 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 ${\stackrel{~}{Z}}_{i}$ can also be obtained by the least-norm least-squares solution of matrix equation ${\sum }_{i=\mathrm{1}}^{t}\mathrm{‍}{M}_{i}{\stackrel{-}{Z}}_{i}{N}_{i}=\stackrel{-}{F}$, in which ${\stackrel{-}{Z}}_{i}={Z}_{i}-{\stackrel{~}{Z}}_{i}\mathrm{, }\mathrm{}\stackrel{-}{F}=F-{\sum }_{i=\mathrm{1}}^{t}\mathrm{‍}{M}_{i}{\stackrel{~}{Z}}_{i}{N}_{i}$. The given numerical examples illustrate the efficiency of this algorithm.

## Citation

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