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

محورهای موضوعی : Linear and multilinear algebra; matrix theory

A. Nazari ¹ , Kh. Sayehvand ² , M. Rostami ³

1 - Department of Mathematics, Arak University, P.O. Box 38156-8-8349, Arak, Iran
2 - Faculty of Mathematical Sciences, University of Malayer, P. O. Box 16846-13114, Malayer, Iran
3 - Faculty of Mathematical Sciences, University of Malayer, P. O. Box 16846-13114, Malayer, Iran

تاریخ دریافت : 1393/07/16 تاریخ پذیرش : 1393/10/27 تاریخ انتشار : 1393/09/10

کلید واژه: fixed point method, Nonlinear matrix equations, Steffensen method,

چکیده مقاله :

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 conditionsthat generate a sequence of positive definite matrices which converges to solutionof this equation.

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