On the Solution of a Class of Nonlinear Systems Governed by an 𝑀-Matrix

We consider a weakly nonlinear system of the form (𝐼+𝜑(𝑥)𝐴)𝑥=𝑝, where 𝜑(𝑥) is a real function of the unknown vector 𝑥, and (𝐼+𝜑(𝑥)𝐴) is an 𝑀-matrix. We propose to solve it by means of a sequence of linear systems defined by the iteration procedure (𝐼+𝜑(𝑥𝑟)𝐴)𝑥𝑟+1=𝑝, 𝑟=0,1,…. The global convergence is...

Full description

Bibliographic Details
Main Authors:	Woula Themistoclakis, Antonia Vecchio
Format:	Article
Language:	English
Published:	Hindawi Limited 2012-01-01
Series:	Discrete Dynamics in Nature and Society
Online Access:	http://dx.doi.org/10.1155/2012/412052

id	doaj-a49fb4847a6a438080f795ff657fa1ce
record_format	Article
spelling	doaj-a49fb4847a6a438080f795ff657fa1ce2020-11-24T22:24:24ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/412052412052On the Solution of a Class of Nonlinear Systems Governed by an 𝑀-MatrixWoula Themistoclakis0Antonia Vecchio1Istituto per le Applicazioni del Calcolo “Mauro Picone”, Sede di Napoli, National Research Council of Italy (CNR), Via P. Castellino, 111, 80131 Napoli, ItalyIstituto per le Applicazioni del Calcolo “Mauro Picone”, Sede di Napoli, National Research Council of Italy (CNR), Via P. Castellino, 111, 80131 Napoli, ItalyWe consider a weakly nonlinear system of the form (𝐼+𝜑(𝑥)𝐴)𝑥=𝑝, where 𝜑(𝑥) is a real function of the unknown vector 𝑥, and (𝐼+𝜑(𝑥)𝐴) is an 𝑀-matrix. We propose to solve it by means of a sequence of linear systems defined by the iteration procedure (𝐼+𝜑(𝑥𝑟)𝐴)𝑥𝑟+1=𝑝, 𝑟=0,1,…. The global convergence is proved by considering a related fixed-point problem.http://dx.doi.org/10.1155/2012/412052
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Woula Themistoclakis Antonia Vecchio
spellingShingle	Woula Themistoclakis Antonia Vecchio On the Solution of a Class of Nonlinear Systems Governed by an 𝑀-Matrix Discrete Dynamics in Nature and Society
author_facet	Woula Themistoclakis Antonia Vecchio
author_sort	Woula Themistoclakis
title	On the Solution of a Class of Nonlinear Systems Governed by an 𝑀-Matrix
title_short	On the Solution of a Class of Nonlinear Systems Governed by an 𝑀-Matrix
title_full	On the Solution of a Class of Nonlinear Systems Governed by an 𝑀-Matrix
title_fullStr	On the Solution of a Class of Nonlinear Systems Governed by an 𝑀-Matrix
title_full_unstemmed	On the Solution of a Class of Nonlinear Systems Governed by an 𝑀-Matrix
title_sort	on the solution of a class of nonlinear systems governed by an 𝑀-matrix
publisher	Hindawi Limited
series	Discrete Dynamics in Nature and Society
issn	1026-0226 1607-887X
publishDate	2012-01-01
description	We consider a weakly nonlinear system of the form (𝐼+𝜑(𝑥)𝐴)𝑥=𝑝, where 𝜑(𝑥) is a real function of the unknown vector 𝑥, and (𝐼+𝜑(𝑥)𝐴) is an 𝑀-matrix. We propose to solve it by means of a sequence of linear systems defined by the iteration procedure (𝐼+𝜑(𝑥𝑟)𝐴)𝑥𝑟+1=𝑝, 𝑟=0,1,…. The global convergence is proved by considering a related fixed-point problem.
url	http://dx.doi.org/10.1155/2012/412052
work_keys_str_mv	AT woulathemistoclakis onthesolutionofaclassofnonlinearsystemsgovernedbyanmmatrix AT antoniavecchio onthesolutionofaclassofnonlinearsystemsgovernedbyanmmatrix
_version_	1725761474078441472

On the Solution of a Class of Nonlinear Systems Governed by an 𝑀-Matrix

Similar Items