Iterative Method for Positive Definite Solution of a Class of Nonlinear Matrix Equation

On positive definite solution of a nonlinear matrix equation

In this paper, an efficient iterative method is presented to solve a new nonlinear matrix equation * r X A X A I   with real matrices and r 1  . Some properties of the positive definite solutions for the nonlinear matrix equation are derived. Moreover, necessary and sufficient conditions for the existence of the positive definite solutions are derived. The error estimation of the iterative m...

On the Positive Definite Solutions of a Nonlinear Matrix Equation

The positive definite solutions of the nonlinear matrix equation Xs + A∗f(X)A = Q are discussed. A necessary and sufficient condition for the existence of positive definite solutions for this equation is derived.Then, the uniqueness of the Hermitian positive definite solution is studied based on an iterative method proposed in this paper. Lastly the perturbation analysis for this equation is di...

Iterative Method for Mirror-Symmetric Solution of Matrix Equation AXB + CY D = E

An Inversion-Free Method for Finding Positive Definite Solution of a Rational Matrix Equation

A new iterative scheme has been constructed for finding minimal solution of a rational matrix equation of the form X + A*X (-1) A = I. The new method is inversion-free per computing step. The convergence of the method has been studied and tested via numerical experiments.

A New Inversion-free Method for Hermitian Positive Definite Solution of Matrix Equation

An inversion-free iterative algorithm is presented for solving nonlinear matrix equation with a stepsize parameter t. The existence of the maximal solution is discussed in detail, and the method for finding it is proposed. Finally, two numerical examples are reported that show the efficiency of the method. Keywords—Inversion-free method, Hermitian positive definite