A block preconditioner for the Gl-LSMR algorithm

The global least squares minimal residual (Gl-LSMR) method is an efficient solver for linear systems with multiple right-hand sides. To accelerate the convergence of the Gl-LSMR method, we propose a block preconditioner for the global LSMR method which can be used for solving linear systems with a block partitioned coefficient matrix and multiple right-hand sides. Numerical examples and comparing the preconditioned Gl-LSMR method with the Gl-LSMR method validate the effectiveness of the preconditioner. Numerical results confirm that the Block Preconditioned Gl-LSMR (BPGLSMR) method has a better performance in reducing the number of iterations and CPU time.