AN ITERATIVE ALGORITHM FOR THE LEAST SQUARES SOLUTIONS OF MATRIX EQUATIONS OVER SYMMETRIC ARROWHEAD MATRICES

- Journal title : Journal of the Korean Mathematical Society
- Volume 52, Issue 2, 2015, pp.349-372
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2015.52.2.349

Title & Authors

AN ITERATIVE ALGORITHM FOR THE LEAST SQUARES SOLUTIONS OF MATRIX EQUATIONS OVER SYMMETRIC ARROWHEAD MATRICES

Ali Beik, Fatemeh Panjeh; Salkuyeh, Davod Khojasteh;

Ali Beik, Fatemeh Panjeh; Salkuyeh, Davod Khojasteh;

Abstract

This paper concerns with exploiting an oblique projection technique to solve a general class of large and sparse least squares problem over symmetric arrowhead matrices. As a matter of fact, we develop the conjugate gradient least squares (CGLS) algorithm to obtain the minimum norm symmetric arrowhead least squares solution of the general coupled matrix equations. Furthermore, an approach is offered for computing the optimal approximate symmetric arrowhead solution of the mentioned least squares problem corresponding to a given arbitrary matrix group. In addition, the minimization property of the proposed algorithm is established by utilizing the feature of approximate solutions derived by the projection method. Finally, some numerical experiments are examined which reveal the applicability and feasibility of the handled algorithm.

Keywords

matrix equation;projection technique;iterative algorithm;least squares problem;arrowhead matrix;

Language

English

Cited by

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