f Toutounian - Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi Univer-sity of Mashhad, Iran.The Center of Excellence on Modelling and Control Systems, Ferdowsi University of Mash-had, Iran.
m Mojarrab - Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi Univer-sity of Mashhad, Iran. Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.

LSMR (Least Squares Minimal Residual) is an iterative method for the solution of the linear system of equations and leastsquares problems. This paper presents a block version of the LSMR algorithm for solving linear systems with multiple right-hand sides. The new algorithm is based on the block bidiagonalization and derived by minimizing the Frobenius norm of the resid ual matrix of normal equations. In addition, the convergence of the proposed algorithm is discussed. In practice, it is also observed that the Frobenius norm of the residual matrix decreases monotonically. Finally, numerical experiments from real applications are employed to verify the effectiveness of the presented method.

LSMR method; Bidiagonalization; Block methods; Iterative methods; Multiple right-hand sides