Two-level least squares methods in Krylov subspaces

Two-level least squares acceleration approaches are applied to Chebyshev acceleration and conjugate residual method with restarts for solving systems of linear algebraic equations with sparse nonsymmetric matrices arising in finite volume or finite element approximations of boundary value problems on irregular grids. Application of the proposed idea to other iterative restarted processes also is considered. The efficiency of the algorithms proposed is investigated numerically on a set of model Dirichlet problems for the convection-diffusion equation.