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S. Karimi and F. Toutounian, “On the Convergence of the BL-LSQR Algorithm for Solving Matrix Equations,” International Journal of Computer Mathematics, Vol. 88, No. 1, 2011, pp. 171-182. doi:10.1080/00207160903365883

has been cited by the following article:

• 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.