A New Iterative Solution Method for Solving Multiple Linear Systems

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.

Conflicts of Interest

The authors declare no conflicts of interest.

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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