Pre-symmetric approach and applications to indefinite non-symmetric problems

A class of pre-symmetric minimal residual method to solve large-scale system of linear algebraic equations with indefinite symmetrizable coefficient matrix is presented in this paper, briefly called as PSMINRES method. The PSMINRES method is established by first transforming the non-symmetric system of equations into symmetric system of equations by the pre-symmetric technique, and then utilizing the minimal residual (MINRES) method to solve the symmetric system of equations and getting a new approximation to the original system of linear equations. Theoretical analysis and numerical computations show that the pre-symmetric technique is feasible and behaviors of the PSMINRES are superior to some Krylov subspace methods, which are usual adopted for solving general non-symmetric linear systems, such as CGS, GMRES, etc.