Alternating Anderson–Richardson method: An efficient alternative to preconditioned Krylov methods for large, sparse linear systems

Comparison of some Preconditioned Krylov Methods for Solving Sparse Non-symmetric Linear Systems of Equations

Large sparse non-symmetric linear systems of equations often occur in many scientific and engineering applications. In this paper, we present a comparative study of some preconditioned Krylov iterative methods, namely CGS, Bi-CGSTAB, TFQMR and GMRES for solving such systems. To demonstrate their efficiency, we test and compare the numerical implementations of these methods on five numerical exa...

Sparse Preconditioned Iterative Methods for Dense Linear Systems

Two sparse preconditioned iterative methods are presented to solve dense linear systems arising in the solution of two dimensional boundary integral equations. In the rst method, the sparse preconditioner is constructedsimply by choosing a small block of elements in the coeecient matrix of a dense linear system. The two-grid method falls into this category when the dense linear system arises fr...

Solving large systems arising from fractional models by preconditioned methods

This study develops and analyzes preconditioned Krylov subspace methods to solve linear systems arising from discretization of the time-independent space-fractional models. First, we apply shifted Grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. Then, we employee two preconditioned iterative methods, namely, the preconditioned gen...

The Improved Krylov Subspace Methods for Large and Sparse Linear Systems on Bulk Synchronous Parallel Architecture

In this paper, we would like to summarize the recent advances on the improved Krylov Subspace methods for the solutions of large and sparse linear systems of equations with unsymmetric coefficient matrices. The proposed methods combine elements of numerical stability and parallel algorithm design without increasing much computational costs. The methods have the following common feature that all...

Preconditioned Krylov Subspace Methods for Eigenvalue Problems