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

الموضوعات :

A. Nazari ¹ (Department of Mathematics, Arak University, P.O. Box 38156-8-8349, Arak, Iran)
Kh. Sayehvand ² (Faculty of Mathematical Sciences, University of Malayer, P. O. Box 16846-13114, Malayer, Iran)
M. Rostami ³ (Faculty of Mathematical Sciences, University of Malayer, P. O. Box 16846-13114, Malayer, Iran)

تاريخ الإرسال : 14 الأربعاء , ذو الحجة, 1435 تاريخ التأكيد : 26 السبت , ربيع الأول, 1436 تاريخ الإصدار : 09 الإثنين , صفر, 1436

الکلمات المفتاحية: fixed point method, Nonlinear matrix equations, Steffensen method,

ملخص المقالة :

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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