CONJUGATE RESIDUAL METHODS FOR ALMOST SYMMETRICAL LINEAR-SYSTEMS

This paper concerns the use of conjugate residual methods for the solution of nonsymmetric linear systems arising in applications to differential equations. We focus on an application derived from a seismic inverse problem. The linear system is a small perturbation to a symmetric positive-definite system, the nonsymmetries arising from discretization errors in the solution of certain boundary-value problems. We state and prove a new error bound for a class of generalized conjugate residual methods; we show that, in some cases, the perturbed symmetric problem can be solved with an error bound similar to the one for the conjugate residual method applied to the symmetric problem. We also discuss several applications for special distributions of eigenvalues.