Numerical methods for differential linear matrix equations via Krylov subspace methods

Krylov subspace methods for projected 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...

Preconditioned Krylov Subspace Methods for Transport Equations

Transport equations have many important applications. Because the equations are based on highly non-normal operators, they present diiculties in numerical computations. The iterative methods have been shown to be one of eecient numerical methods to solve transport equations. However, because of the nature of transport problems, convergence of iterative methods tends to slow for many important p...

Krylov subspace methods for solving linear systems

Inexact Krylov Subspace Methods for Linear Systems

There is a class of linear problems for which the computation of the matrix-vector product is very expensive since a time consuming approximation method is necessary to compute it with some prescribed relative precision. In this paper we investigate the effect of an approximately computed matrix-vector product on the convergence and accuracy of several Krylov subspace solvers. The obtained insi...

Numerical Methods for Fuzzy Linear Partial Differential Equations under new Definition for Derivative

In this paper difference methods to solve "fuzzy partial differential equations" (FPDE) such as fuzzy hyperbolic and fuzzy parabolic equations are considered. The existence of the solution and stability of the method are examined in detail. Finally examples are presented to show that the Hausdorff  distance between the exact solution and approximate solution tends to zero.