Preconditioned gradient type methods applied to nonsymmetric linear systems

Preconditioned gradient type iterative techniques have been proved to be powerful methods for solving large systems of nonsymmetric linear equations. This paper, which is concerned with the truncated generalized conjugate residual algorithms for solving such problems, introduces an approximate preconditioning strategy. This strategy is particularly attractive for matrices resulting from high order numerical approximations applied to elliptic partial differential equations. Numerical results demonstrate that the preconditioned iterative scheme is efficient, and it requires the same amount of computational work per iteration as the preconditioned conjugate gradient method for symmetric and positive definite matrices.