J. Korean Math. Soc. 2015; 52(2): 349-372
Printed March 1, 2015
https://doi.org/10.4134/JKMS.2015.52.2.349
Copyright © The Korean Mathematical Society.
Fatemeh Panjeh Ali Beik and Davod Khojasteh Salkuyeh
Vali-e-Asr University of Rafsanjan, University of Guilan
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
MSC numbers: Primary 15A24, 65F10
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