On the convergence of the Bl-LSQR algorithm for solving matrix equations

Abstract

Karimi and Toutounian [The block least squares method for solving nonsymmetric linear system with multiple right-hand sides, Appl. Math. Comput. 177 (2006), pp. 852–862], proposed a block version of the LSQR algorithm, say Bl-LSQR, for solving linear system of equations with multiple right-hand sides. In this paper, the convergence of the Bl-LSQR algorithm is studied. We deal with some computational aspects of the Bl-LSQR algorithm for solving matrix equations. Some numerical experiments on test matrices are presented.

Keywords:

• block methods
• iterative method
• multiple right-hand sides
• LSQR
• Bl-LSQR

2010 AMS Subject Classifications :

• 65F10
• 65F50
• 65N22

Acknowledgements

The authors are grateful to the anonymous referees for their comments which substantially improved the quality of this paper.