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A New Iterative Solution Method for Solving Multiple Linear Systems
Department of Mathematics, Persian Gulf University, Bushehr, Iran
- 1 Department of Mathematics, Persian Gulf University, Bushehr, Iran
Advances in Linear Algebra & Matrix Theory·Volume 02 (2012)·Pages 25–30·Published 24 September 2012·DOI10.4236/alamt.2012.23004
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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.
KeywordsIterative MethodMultiple Linear SystemsLSQR MethodGL-LSQR MethodProjection Method
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