A New Iterative Solution Method for Solving Multiple Linear Systems

Saeed Karimi

Department of Mathematics, Persian Gulf University, Bushehr, Iran.

DOI: 10.4236/alamt.2012.23004                

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.

Keywords

Iterative Method; Multiple Linear Systems; LSQR Method; GL-LSQR Method; Projection Method

Conflicts of Interest

The authors declare no conflicts of interest.

References

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