SIAM Journal on Scientific Computing

The Arnoldi iteration, usually viewed as a method for calculating eigenvalues, can also be used to estimate pseudospectra. This possibility may be of practical importance, because in applications involving highly nonnormal matrices or operators, such as ...

An inexact Newton method is a generalization of Newton’s method for solving $F(x) = 0,F:\mathbb{R}^n \to \mathbb{R}^n $in which, at the kth iteration, the step $s_k $ from the current approximate solution $x_k $ is required to satisfy a condition $\|F(x_...

Discretization and linearization of the steady–state Navier-Stokes equations gives rise to a nonsymmetric indefinite linear system of equations. In this paper, we introduce preconditioning techniques for such systems with the property that the eigenvalues ...

A semi-Toeplitz preconditioner for nonsymmetric, nondiagonally dominant systems of equations is studied. The preconditioner solve is based on a fast modified sine transform. As a model problem we study a system of equations arising from an implicit time ...

Timestepping to a steady-state solution is increasingly applied in engineering and scientific applications as a means for solving equilibrium problems. In the present work we examine the relation between the recursion in timestepping algorithms for ...

The discrete-dipole approximation (DDA) is a method for calculating the scattering of light by an irregular particle. The DDA has been used, for example, in calculations of optical properties of cosmic dust. In this method the particle is approximated by ...

In this paper we propose and discuss two preconditioners for boundary integral equations on domains that are nearly symmetric. The preconditioners under consideration are equivariant; that is, they commute with a group of permutation matrices. Numerical ...

Due to memory limitations, iterative methods have become the method of choice for large scale semiconductor device simulation. However, it is well known that these methods suffer from reliability problems. The linear systems that appear in numerical ...

A multigrid preconditioned conjugate gradient algorithm is introduced into a semiconductor device modeling code DANCIR. This code simulates a wide variety of semiconductor devices by numerically solving the drift-diffusion equations. The most time-...

The efficiency of numerically solving time-dependent partial differential equations on parallel computers can be greatly improved by computing the solution on many time levels simultaneously. The theoretical properties of one such method, namely the ...

Extrapolation methods for the solution of partial differential equations are commonly based on the existence of error expansions for the approximate solution. Implicit extrapolation, by contrast, is based on applying extrapolation indirectly, by using it ...

Optimal relaxation parameters are obtained for red-black Gauss–Seidel relaxation in multigrid solvers of a family of elliptic equations. The resulting relaxation schemes are found to retain very high efficiency over an appreciable range of coefficients of ...

The sampled Radon transform of a two-dimensional (2D) function can be represented as a continuous linear map $A:L_2 (\Omega ) \to {\bf R}^N $, where $(Au)_j = (u,\psi _j )$ and $\psi _j $ is the characteristic function of a strip through $\Omega $ ...

In this paper we show how the properties of integral operators and their approximations are reflected in the performance of the GMRES iteration and how these properties can be used to smooth the GMRES iterates by an implicit application of Nyström ...

Total variation (TV) methods are very effective for recovering “blocky,” possibly discontinuous, images from noisy data. A fixed point algorithm for minimizing a TV penalized least squares functional is presented and compared with existing minimization ...

Distributed-memory parallel processors (DMPPs) can deliver peak performance higher than vector supercomputers while promising a better cost-performance ratio. Programming, however, is harder than on traditional vector systems, especially when problems ...

In this paper, we show a simple parallel algorithm for polynomial evaluation. By this method, we only need ${{2N} / p} + \log _2 p$ steps on p processors (where $p \leqslant O(N^{{1 / 2}} )$) to evaluate a polynomial of degree N on an SIMD computer or an ...

The solution of complex symmetric indefinite systems of equations where multiple solutions are required is considered. The quasi-minimum residual (QMR) method, ideally suited for these matrices, is generalized using the block Lanczos algorithm to solve ...

In 1980, S.-P. Han [Least-Squares Solution of Linearlnequalities, Tech. Report TR–2141, Mathematics Research Center, University of Wisconsin-Madison, 1980] described a finitely terminating algorithm for solving a system $Ax \leqslant b$ of linear ...

Iterative aggregation–disaggregation (IAD) is an effective method for solving finite nearly completely decomposable (NCD) Markov chains. Small perturbations in the transition probabilities of these chains may lead to considerable changes in the stationary ...