Regularized conjugate gradient method for skew-symmetric indefinite system of linear equations and applications

A class of regularized conjugate gradient methods is presented for solving large-scale sparse system of linear equations of which the coefficient matrix is an ill-conditioned skew-symmetric indefinite matrix. The convergence is proved and the possible choices of the parameters involved in the new methods are discussed in detail. Preliminary numerical computations show that the numerical behaviors of the new methods are superior to those of some standard Krylov subspace methods, such as CGNE, CGS, GMRES etc.