‎in this paper‎, ‎we propose two preconditioned aor iterative methods to solve systems of linear equations whose coefficient matrices are z-matrix‎. ‎these methods can be considered as improvements of two previously presented ones in the literature‎. ‎finally some numerical experiments are given to show the effectiveness of the proposed preconditioners‎.‎

Based on the Hermitian and skew-Hermitian splitting (HSS) iteration technique, we establish a generalized HSS (GHSS) iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and positive definite/semidefinite matrices. The GHSS method is essentially a four-parameter iteration which not only covers the standard HSS iteration but also enables us to optimize the ...

This paper is concerned with the mixed H2/H∞ control problem via static output feedback control. The main purpose of this paper is to give an iterative method for finding a sub-optimal static output-feedback controller for the mixed H2/H∞ control problem. The contribution of this paper is to derive a gradient of the H2 cost function. Using this gradient, we propose a gradient method for H2 and ...

We discuss certain preconditioning techniques for solving indefinite linear systems of equations arising from mixed finite element discretizations of elliptic equations of second order. The techniques are based on various approximations of the mass matrix, say, by simply lumping it to be diagonal or by constructing a diagonal matrix assembled of properly scaled lumped element mass matrices. We ...

This paper presents an overview and comparison of iterative solvers for linear stochastic partial differential equations (PDEs). A stochastic Galerkin finite element discretization is applied to transform the PDE into a coupled set of deterministic PDEs. Specialized solvers are required to solve the very high-dimensional systems that result after a finite element discretization of the resulting...

A 2nd-order, L-stable Rosenbrock method from the eld of sti ordinary di erential equations is studied for application to atmospheric dispersion problems describing photochemistry, advective and turbulent di usive transport. Partial di erential equation problems of this type occur in the eld of air pollution modelling. The focal point of the paper is to examine the Rosenbrock method for reliable...

A new numerical scheme based on the H-Galerkin mixed finite element method for a class of second-order pseudohyperbolic equations is constructed. The proposed procedures can be split into three independent differential sub-schemes and does not need to solve a coupled system of equations. Optimal error estimates are derived for both semidiscrete and fully discrete schemes for problems in one spa...