Krylov subspace methods for solving large unsymmetric linear systems

Some algorithms based upon a projection process onto the Krylov subspace are developed, generalizing the method of conjugate gradients to unsymmetric systems. These methods are extensions of Arnoldis algorithm for solving eigenvalue problems. The convergence is analyzed in terms of the distance of the solution to the subspace Km and some error bounds are established showing, in particular, a similarity with the conjugate gradient method (for symmetric matrices) when the eigenvalues are real. Several numerical experiments are described and discussed.