A New Iterative Solution Method for Solving Multiple Linear Systems
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.
Cite this paper: S. Karimi, "A New Iterative Solution Method for Solving Multiple Linear Systems," Advances in Linear Algebra & Matrix Theory, Vol. 2 No. 3, 2012, pp. 25-30. doi: 10.4236/alamt.2012.23004.
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