Least squares methods in Krylov subspaces

The paper considers iterative algorithms for solving large systems of linear algebraic equations with sparse nonsymmetric matrices based on solution of least squares problems in Krylov subspaces and generalizing the alternating Anderson–Jacobi method. The approaches suggested are compared with the classical Krylov methods, represented by the method of semi-conjugate residuals. The efficiency of parallel implementation and speedup are estimated and illustrated with numerical results obtained for a series of linear systems resulting from discretization of convection-diffusion boundary-value problems.