This paper is devoted to the numerical solution of projected generalized continuous-time Lyapunov equations with low-rank right-hand sides. Such equations arise in stability analysis and control problems for descriptor systems including model reduction based on balanced truncation. A parameter free iterative method is proposed. This method is based upon a combination of an approximate power met...

Based on a group of new Saul’yev type asymmetric difference schemes constructed by author, a high-order, unconditionally stable and parallel alternating segment explicit-implicit method for the numerical solution of the fourth-order heat equation is derived in this paper. The truncation error is fourth-order in space, which is much more accurate than the known alternating segment explicit-impli...

In the present paper we consider a 2-D shallow-water equations (SWE) model on a βplane solved using an alternating direction fully implicit (ADI) finite-difference scheme (Gustafsson 1971, Fairweather and Navon 1980, Navon and De Villiers 1986, Kreiss and Widlund 1966) on a rectangular domain. The scheme was shown to be unconditionally stable for the linearized equations. The discretization yie...

Among various studies for color image denoising, the methods based on the chromaticity-brightness decomposition are known to result in relatively better restored images. This article begins with a generalization of the chromaticitybrightness model in the angle domain, hybridizing the total-variation minimization and the mean-curvature flow. For a reliable preservation of the edges, we suggest a...

In this paper, we present a novel iterative numerical solution to the Poisson equation whose solution is needed in a variety of low-level vision problems. Our algorithm is an O(N) (N being the number of discretization points) iterative technique and does not make any assumptions on the shape of the input domain unlike the polyhedral domain assumption in the proof of convergence of multi-grid te...

Fractional differential equations have attracted considerable interest because of their ability to model anomalous transport phenomena. Fractional nonlinear reaction-diffusion models have found numerous applications in patten formation in biology, chemistry, physics and Engineering. Obtaining analytical solutions of fractional nonlinear reaction-diffusion models is difficult, generally numerica...

In this paper we consider the numerical solution of projected generalized continuous-time Lyapunov equations with low-rank right-hand sides. The interest in this problem stems from stability analysis and control problems for descriptor systems including model reduction based on balanced truncation. Two projection methods are proposed for calculating low-rank approximate solutions. One is based ...

1. Introduction. In companion papers [l; 6] recently Peaceman, Rachford, and the author introduced a finite difference technique called therein the alternating direction implicit method for approximating the solution of transient and permanent heat flow problems in two space variables. The validity of the method was established only in the case of a rectangular domain. Since then the procedure ...

Low-rank iterative methods of periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems Low-rank iterative methods of periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems Abstract We discuss the numerical solution of large-scale sparse projected discrete-time periodic Lyapunov equations ...

We consider the numerical solution of projected Lyapunov equations using Krylov subspace iterative methods. Such equations play a fundamental role in balanced truncation model reduction of descriptor systems. We present generalizations of the extended block and global Arnoldi methods to projected Lyapunov equations and compare these methods with the alternating direction implicit method with re...