Some Iterative Methods for Solving Nonlinear Matrix Equations

2014 ◽  
Author(s):  
A. Cordero ◽  
J.R. Torregrosa ◽  
M.P. Vassileva
Keyword(s):  
Iterative Methods ◽  
Matrix Equations ◽  
Nonlinear Matrix

scholarly journals Positive coincidence points for a class of nonlinear operators and their applications to matrix equations

2020 ◽  
Vol 18 (1) ◽  
pp. 858-872
Author(s):  
Imed Kedim ◽  
Maher Berzig ◽  
Ahdi Noomen Ajmi
Keyword(s):  
Banach Space ◽  
Positive Solution ◽  
Positive Definite ◽  
Positive Cone ◽  
Matrix Equations ◽  
Ordered Banach Space ◽  
Coincidence Points ◽  
Nonlinear Operators ◽  
Nonlinear Matrix

Abstract Consider an ordered Banach space and f,g two self-operators defined on the interior of its positive cone. In this article, we prove that the equation f(X)=g(X) has a positive solution, whenever f is strictly \alpha -concave g-monotone or strictly (-\alpha ) -convex g-antitone with g super-homogeneous and surjective. As applications, we show the existence of positive definite solutions to new classes of nonlinear matrix equations.

scholarly journals Common Fixed-Point Results in Ordered Left (Right) Quasi- b -Metric Spaces and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Hemant Kumar Nashine ◽  
Sourav Shil ◽  
Hiranmoy Garai ◽  
Lakshmi Kanta Dey ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Matrix Equations ◽  
Ordered Sets ◽  
Nonlinear Matrix ◽  
Fractional Differential ◽  
Left And Right

We use the notions of left- and right-complete quasi- b -metric spaces and partial ordered sets to obtain a couple of common fixed-point results for strictly weakly isotone increasing mappings and relatively weakly increasing mappings, which satisfy a pair of almost generalized contractive conditions. To illustrate our results, throughout the paper, we give several relevant examples. Further, we use our results to establish sufficient conditions for existence and uniqueness of solution of a system of nonlinear matrix equations and a pair of fractional differential equations. Finally, we provide a nontrivial example to validate the sufficient conditions for nonlinear matrix equations with numerical approximations.

scholarly journals Best Proximity Point Results for Generalized Θ-Contractions and Application to Matrix Equations

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 93
Author(s):  
Zhenhua Ma ◽  
Azhar Hussain ◽  
Muhammad Adeel ◽  
Nawab Hussain ◽  
Ekrem Savas
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Positive Definite ◽  
Matrix Equations ◽  
Nonlinear Matrix Equation ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Positive Definite Solution ◽  
Nonlinear Matrix ◽  
Definite Solution

In this paper, we introduce the notion of C ´ iri c ´ type α - ψ - Θ -contraction and prove best proximity point results in the context of complete metric spaces. Moreover, we prove some best proximity point results in partially ordered complete metric spaces through our main results. As a consequence, we obtain some fixed point results for such contraction in complete metric and partially ordered complete metric spaces. Examples are given to illustrate the results obtained. Moreover, we present the existence of a positive definite solution of nonlinear matrix equation X = Q + ∑ i = 1 m A i * γ ( X ) A i and give a numerical example.

scholarly journals Generalized Inverses Estimations by Means of Iterative Methods with Memory

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 2
Author(s):  
Santiago Artidiello ◽  
Alicia Cordero ◽  
Juan R. Torregrosa ◽  
María P. Vassileva
Keyword(s):  
Iterative Methods ◽  
Generalized Inverses ◽  
Drazin Inverse ◽  
Nonsingular Matrix ◽  
Type Method ◽  
The Matrix ◽  
Nonlinear Matrix ◽  
First Time ◽  
With Memory ◽  
Theoretical Results

A secant-type method is designed for approximating the inverse and some generalized inverses of a complex matrix A. For a nonsingular matrix, the proposed method gives us an approximation of the inverse and, when the matrix is singular, an approximation of the Moore–Penrose inverse and Drazin inverse are obtained. The convergence and the order of convergence is presented in each case. Some numerical tests allowed us to confirm the theoretical results and to compare the performance of our method with other known ones. With these results, the iterative methods with memory appear for the first time for estimating the solution of a nonlinear matrix equations.

Sign in / Sign up

Export Citation Format

Share Document