GMRES and CGS are well-known iterative methods for the solution of certain sparse linear systems with a non-symmetric matrix. These methods have been compared experimentally in many studies and speciic observations on their convergence behaviour have been reported. A new iterative method to solve a non-symmetric system is proposed by Eirola and Nevanlinna. The purpose of this paper is to invest...

In this paper, a two-stage iterative algorithm is proposed to improve the convergence of Krylov based iterative methods, typically those of GMRES variants. The principle of the proposed approach is to build an external iteration over the Krylov method, and to frequently store its current residual (at each GMRES restart for instance). After a given number of outer iterations, a least-squares min...

In this paper we derive convergence estimates for the iterative solution of nonsymmetric linear systems by GMRES. We work in the context of strongly convergent-collectively compact sequences of approximations to linear compact xed point problems. Our estimates are intended to explain the observations that the performance of GMRES is independent of the discretization if the resolution of the dis...

Over the past several years a number of hybrid algorithms have been proposed for solving large sparse systems of linear algebraic equations. In this paper we consider the hybrid GMRES algorithm by Nachtigal, Reichel and Trefethen (1992) and show that in the floating-point arithmetic there exist some cases in which the properties of this algorithm are lost, e.g., the result is false, or the coef...

In this work, a two-layer coupled fluid-structure-structure interaction model is considered, which incorporates an anisotropic structure model into the fluid-structure interaction problems. We propose two domain decomposition solvers for such a class of coupled problems: a Robin-Robin preconditioned GMRES solver combined with an inner Dirichlet-Neumann iterative solver, and a Robin-Robin precon...

The GMRES method for solving nonsymmetric linear equations is generally used with restarting to reduce storage and orthogonalization costs. Restarting slows down the convergence. However, it is possible to save some important information at the time of the restart. It is proposed that approximate eigenvectors corresponding to a few of the smallest eigenvalues be formed and added to the subspace...

We look at multigrid methods for unsteady viscous compressible flows. We specifically target smoothers that can be used in parallel and without computation of a Jacobian, which are particlarly attractive candidates in the context of Discontinuous Galerkin discretizations. In CFD, a plethora of nonlinear smoothers have been suggested which are hard to analyze. Our methodology is to use a linear ...