PERTURBATION ANALYSIS OF A NONLINEAR MATRIX EQUATION

Perturbation analysis of nonlinear matrix population models

Perturbation analysis examines the response of a model to changes in its parameters. It is commonly applied to population growth rates calculated from linear models, but there has been no general approach to the analysis of nonlinear models. Nonlinearities in demographic models may arise due to density-dependence, frequency-dependence (in 2-sex models), feedback through the environment or the e...

Perturbation Analysis for the Matrix Equation X − ∑

A Solution of Riccati Nonlinear Differential Equation using Enhanced Homotopy Perturbation Method (EHPM)

Homotopy Perturbation Method is an effective method to find a solution of a nonlinear differential equation, subjected to a set of boundary condition. In this method a nonlinear and complex differential equation is transformed to series of linear and nonlinear and almost simpler differential equations. These set of equations are then solved secularly. Finally a linear combination of the solutio...

Perturbation Estimates for the Maximal Solution of a Nonlinear Matrix Equation∗

In this paper a nonlinear matrix equation is considered. Perturbation estimations for the maximal solution of the considered equation are obtained. The results are illustrated by the use of numerical examples. MSC: 65F10; 15A24 keywords: nonlinear matrix equation, perturbation estimates

Steffensen method for solving nonlinear matrix equation $X+A^T X^{(-1)}A=Q$

In this article we study Steffensen method to solve nonlinear matrix equation $X+A^T X^{(-1)}A=Q$, when $A$ is a normal matrix. We establish some conditions that generate a sequence of positive denite matrices which converges to solution of this equation.