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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/412052 |
| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |