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Developing the CGLS algorithm for the least squares solutions of the general coupled matrix equations
Author(s) -
Hajarian Masoud
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3017
Subject(s) - mathematics , conjugate gradient method , iterative method , norm (philosophy) , least squares function approximation , matrix norm , matrix (chemical analysis) , mathematical optimization , algorithm , eigenvalues and eigenvectors , statistics , physics , materials science , quantum mechanics , estimator , political science , law , composite material
In the present paper, we consider the minimum norm solutions of the general least squares problem∑ j = 1 qA 1 , jX jB 1 , j∑ j = 1 qA 2 , jX jB 2 , j⋮∑ j = 1 qA p , jX jB p , j−C 1C 2⋮C p= min . By developing the conjugate gradient least square (CGLS) method, we construct an efficient iterative method to solve this problem. The constructed iterative method can compute the solution group of the problem within a finite number of iterations in the absence of roundoff errors. Also it is shown that the method is stable and robust. Finally, by some numerical experiments, we demonstrate that the iterative method is effective and efficient. Copyright © 2013 John Wiley & Sons, Ltd.