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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/412052 |
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| author | Woula Themistoclakis Antonia Vecchio |
| author_facet | Woula Themistoclakis Antonia Vecchio |
| author_sort | Woula Themistoclakis |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-a49fb4847a6a438080f795ff657fa1ce |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-a49fb4847a6a438080f795ff657fa1ce2025-02-03T00:59:53ZengWileyDiscrete 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2012/412052 |
| work_keys_str_mv | AT woulathemistoclakis onthesolutionofaclassofnonlinearsystemsgovernedbyanmmatrix AT antoniavecchio onthesolutionofaclassofnonlinearsystemsgovernedbyanmmatrix |