A preconditioned AOR iterative method is proposed with the preconditioner I + S∗ αβ. Some comparison theorems are given when the coefficient matrix of linear system A is an irreducible L−matrix. The convergence rate of AOR iterative method with the preconditioner I + S∗ αβ is faster than the convergence rate with the preconditioner I + Sα by Li et al. Numerical example verifies comparison theor...

In this paper, we develop a new block triangular preconditioner for solving partial differential equations with random coefficients. We prove spectral bounds the preconditioned system. Several numerical examples are provided to demonstrate efficiency of preconditioner, especially stochastic problems large variance.

This paper introduces the recursive sweeping preconditioner for the numerical solution of the Helmholtz equation in three dimensions. This is based on the earlier work of the sweeping preconditioner with the moving perfectly matched layers. The key idea is to apply the sweeping preconditioner recursively to the quasi-two-dimensional auxiliary problems introduced in the three-dimensional (3D) sw...

The generalized Davidson algorithm can be seen as a method which uses preconditioned residuals to create a subspace where it is easier to nd the smallest eigenvalue and its eigenvector. In this paper theoretical results proving convergence rates are shown. In addition, we investigate the use of multigrid as a preconditioner for this method and describe a new algorithm for calculating some other...

We consider Newton-Krylov methods for solving discretized compressible Euler equations. A good preconditioner in the Krylov subspace method is crucial for the efficiency of the solver. In this paper we consider a point-block Gauss-Seidel method as preconditioner. We describe and compare renumbering strategies that aim at improving the quality of this preconditioner. A variant of reordering meth...

A preconditioner for iterative solution of the interface problem in Schur Complement Domain Decomposition Methods is presented. This preconditioner is based on solving a problem in a narrow strip around the interface. It requires much less memory and computing time than classical Neumann-Neumann preconditioner and its variants, and handles correctly the flux splitting among subdomains that shar...

The boundary integral method is an efficient approach for solving time-harmonic obstacle scattering problems from bounded scatterers. This paper presents the directional preconditioner for the linear systems of the boundary integral method in two dimensions. This new preconditioner builds a data-sparse approximation of the integral operator, transforms it into a sparse linear system, and comput...

We present a new parallelizable preconditioner that is used as the local component for a two-level preconditioner similar to BPS. On 2D model problems that exhibit either high anisotropy or discontinuity, we demonstrate its attracting numerical behaviour and compare it to the regular BPS. Finally, to alleviate the construction cost of this new preconditioner, that requires the explicit computat...

T paper is the experimental follow-up to Langville and Stewart (2002), where the theoretical background for the nearest Kronecker product (NKP) preconditioner was developed. Here we test the NKP preconditioner on both Markov chains (MCs) and stochastic automata networks (SANs). We conclude that the NKP preconditioner is not appropriate for general MCs, but is very effective for a MC stored as a...