On the Solution of a Class of Nonlinear Systems Governed by an M‐Matrix | Zendy

Woula Themistoclakis | Zendy; Antonia Vecchio | Zendy

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

Author(s) -

Woula Themistoclakis,

Antonia Vecchio

Publication year - 2012

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2012/412052

Subject(s) - mathematics , sequence (biology) , convergence (economics) , class (philosophy) , nonlinear system , matrix (chemical analysis) , fixed point , function (biology) , vector valued function , pure mathematics , mathematical analysis , combinatorics , computer science , physics , genetics , materials science , quantum mechanics , artificial intelligence , evolutionary biology , economics , composite material , biology , economic growth

We consider a weakly nonlinear system of the form (+())=, where () is a real function of the unknown vector , and (+()) is an -matrix. We propose to solve it by means of a sequence of linear systems defined by the iteration procedure (+())+1=, =0,1,…. The global convergence is proved by considering a related fixed-point problem

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