A block conjugate gradient method applied to linear systems with multiple right-hand sides Original Research Article

With the generalization of the Conjugate Gradient (CG) method, a Block CG (BCG) is presented in this paper, which can simultaneously solve symmetric and positive definite linear systems with multiple right-hand sides and still preserves all the properties of the standard CG method. Several techniques related to the efficiency enhancement of BCG, including initial residual vectors orthogonalization and flexible convergence control, are also proposed. Finally, the performances of BCG are investigated on three numerical examples. In these cases improvements between 30% and 200% in terms of both CPU time and iteration requirements are achieved by the BCG method in comparison with the standard CG approach.