We prove a convergence result for an iterative method, proposed recently by B. Meini, for finding the maximal Hermitian positive definite solution of the matrix equationX+A∗X−1A = Q, where Q is Hermitian positive definite.
This paper is concerned with numerical solutions to general linear matrix equations including the wellknown Lyapunov matrix equation and Sylvester matrix equation as special cases. Gradient based iterative algorithm is proposed to approximate the exact solution. A necessary and s
where T = M-'N. In this article we consider solutions of (1.1) where A is a singular operator and f is such that a solution exists, i.e., consistent singular systems. Singular systems of linear equations appear in many applications, such as when computing the stationary probabili
In this paper, an iterative method to solve one kind of nonlinear matrix equation is discussed. For each initial matrix with some conditions, the matrix sequences generated by the iterative method are shown to lie in a fixed open ball. The matrix sequences generated by the iterat
This work proposes proposed a technique inspired by memetic algorithm (MA) to improve the convergence of iterative methods for solving systems of equations. In the first phase the system of equations is transformed into an optimization problem. In this first phase, a memetics tec
This paper treats a set of equations of the form X + AF(X)A = Q, where F maps positive definite matrices either into positive definite matrices or into negative definite matrices, and satisfies some monotonicity property. Here A is arbitrary and Q is a positive definite matrix. I
Singular systems with index one arise in many applications, such as Markov chain modelling. In this paper, we use the group inverse to characterize the convergence and quotient convergence properties of stationary iterative schemes for solving consistent singular linear systems w