Triangular skew-symmetric iterative solvers for strongly nonsymmetric positive real linear system of equations Original Research Article

A new class of triangular iterative methods for solving nonsymmetric linear systems of equations with strongly nonsymmetric positive real matrices is proposed. The triangular operator of these iterative methods uses the skew-symmetric part of the initial matrix. For the new methods, a convergence analysis, a technique for choosing the optimal parameter, and an accelerating procedure are presented. Several numerical experiments include the solution of the strongly nonsymmetric linear systems arising from a central finite-difference approximation of the steady convection–diffusion equation with the Peclet numbers Pe=103, 104, and 105. The relative performance of these methods is compared to the popular SOR procedure.