Two Conjugate-Gradient-Type Methods for Unsymmetric Linear Equations
We propose two new conjugate-gradient-type methods for the solution of sparse unsymmetric linear systems. We present a new tridiagonalization process for unsymmetric matrices that is closely related to the Lanczos process. We use orthogonal factorizations of the tridiagonal matrix to derive the new algorithms USYMLQ and USYMQR in the same fashion as SYMMLQ and MINRES [C. C. Paige and M. A. Saunders, “Solution of sparse indefinite systems of linear equations,” SIAM J. Numer. Anal., 12 (1975), pp. 617–629], for symmetric matrices. Some numerical results for the new methods and comparisons with other methods are presented.