In this work we calculate the eigenvalues obtained by preconditioning the discrete Helmholtz operator with Sommerfeld-like boundary conditions on a rectilinear domain, by a related operator with boundary conditions that permit the use of fast solvers. The main innovation is that the eigenvalues for two and three-dimensional domains can be calculated exactly by solving a set of one-dimensional e...

This paper presents a new preconditioning technique for the restarted GMRES algorithm. It is based on an invariant subspace approximation which is updated at each cycle. Numerical examples show that this deea-tion technique gives a more robust scheme than the restarted algorithm, at a low cost of operations and memory.

In this paper we show how the properties of integral operators and their approximations are reeected in the performance of the GMRES iteration and how these properties can be used to smooth the GMRES iterates, thereby strengthening the norm in which convergence takes place. The smoothed iteration has very similar properties to Broyden's method and we present some comparisons of the two methods ...

The GMRES and Arnoldi algorithms, which reduce to the CR and Lanczos algorithms in the symmetric case, both minimize p(A)b over polynomials p of degree n. The difference is that p is normalized at z 0 for GMRES and at z x for Arnoldi. Analogous "ideal GMRES" and "ideal Arnoldi" problems are obtained if one removes b from the discussion and minimizes p(/l)II instead. Investigation of these true ...

This paper is intended to propose a method to replace the original fuzzy linear system by two crisp linear systems. And then, the method is implemented by GMRES. If a fuzzy nonsingular linear system has a fuzzy solution, our method is able to obtain the solution. Otherwise, our method can only find a weak fuzzy solution. At last, some large scale numerical tests are presented.

Saddle-point systems, i.e., structured linear systems with symmetric matrices are considered. A modified implementation of (preconditioned) MINRES is derived which allows subvectors of the residual to be monitored individually. Compared to the implementation from the textbook of [Elman, Silvester and Wathen, Oxford University Press, 2014], our method requires one extra vector of storage and no ...

This paper is devoted to the analysis of the behaviour, in nite precision arithmetic, of the quasi-minimal residual method without look ahead for the solution of linear systems Ax = b where A is a real or complex matrix of order n. In exact arithmetic, the behaviour of the method as applied to symmetric deenite matrices is well understood; but results about convergence usually suppose that the ...

We provide formulas for the norm of the error when solving non symmetric linear systems with the full orthogonalization method (FOM) and the generalized minimum residual method (GMRES) as well as relations between the error norm and the residual norm. From these formulas we are able to compute estimates of the norm of the error during the iterations. Since stopping criteria based on the norm of...

agricultural extension workers’ service has been placed as the central pattern of agricultural transformation in general and smallholder farmers in particular. due largely to this commensurately known trend, identifying factors that determine farmers’ access to extension workers’ service and the effect of the service on crop yield was found to be imperative. cross sectional data was collected t...