A BLOCK CONJUGATE-GRADIENT METHOD APPLIED TO LINEAR-SYSTEMS WITH MULTIPLE RIGHT-HAND SIDES

With the generalization of the Conjugate Gradient (CG) method, a Block CG (BCG) is presented in this paper, which can simultaneously solve s ymmetric and positive definite linear systems with multiple right-hand sides and still preserves all the properties of the standard CG metho d. Several techniques related to the efficiency enhancement of BCG, in cluding initial residual vectors orthogonalization and flexible conver gence 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 requirem ents are achieved by the BCG method in comparison with the standard CG approach.