A variant of Newton's method for generalized equations
In this article, we study a variant of Newton's method of the following form 0 ε f(x k) + hΔf(x k k)(x k+1 - x k) + F(x k+1) where f is a function whose Frechet derivative is K-lipschitz, F is a set-valued map between two Banach spaces X and Y and h is a constant. We prove that this method is locally convergent to x* a solution of 0 ε f(x) + F(x), if the set-valued map [f(x*) + hΔf(x*)(.- x*) + F(.)]-1 is Aubin continuous at (0, x*) and we also prove the stability of this method.
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| Main Authors: | , |
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| Format: | Digital revista |
| Language: | English |
| Published: |
Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas
2005
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| Online Access: | http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262005000200003 |
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