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http://dx.doi.org/10.4134/JKMS.2015.52.2.349

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

Ali Beik, Fatemeh Panjeh (Department of Mathematics Vali-e-Asr University of Rafsanjan)
Salkuyeh, Davod Khojasteh (Faculty of Mathematical Sciences University of Guilan)
Publication Information
Journal of the Korean Mathematical Society / v.52, no.2, 2015 , pp. 349-372 More about this Journal
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;
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