Preconditioned Conjugate-Gradient Methods for Nonsymmetric Systems of Linear Equations.

In this paper, we present a class of iterative descent methods for solving large, sparse, nonsymmetric systems of linear equations whose coefficient matrices have positive-definite symmetric parts. Such problems commonly arise from the discretization of non-self-adjoint elliptic partial differential equations. The methods we consider are modelled after the conjugate gradient method. They require no estimation of parameters and their rate of convergence appears to depend on the spectrum of A rather than ATA. Their convergence can also be accelerated by preconditioning techniques.