TITLE:
A New Iterative Solution Method for Solving Multiple Linear Systems
AUTHORS:
Saeed Karimi
KEYWORDS:
Iterative Method; Multiple Linear Systems; LSQR Method; GL-LSQR Method; Projection Method
JOURNAL NAME:
Advances in Linear Algebra & Matrix Theory,
Vol.2 No.3,
September
24,
2012
ABSTRACT: In this paper, a new iterative solution method is proposed for solving multiple linear systems A(i)x(i)=b(i), for 1≤ i ≤ s, where the coefficient matrices A(i) and the right-hand sides b(i) are arbitrary in general. The proposed method is based on the global least squares (GL-LSQR) method. A linear operator is defined to connect all the linear systems together. To approximate all numerical solutions of the multiple linear systems simultaneously, the GL-LSQR method is applied for the operator and the approximate solutions are obtained recursively. The presented method is compared with the well-known LSQR method. Finally, numerical experiments on test matrices are presented to show the efficiency of the new method.