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Relaxing the convergence conditions for Newton-like methods

✍ Scribed by Ioannis K. Argyros

Publisher
Springer-Verlag
Year
2006
Tongue
English
Weight
179 KB
Volume
21
Category
Article
ISSN
1598-5865

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The classical Kantorovich theorem on Newton's method assumes that the first 5 w Ž . derivative of the operator involved satisfies a Lipschitz condition ⌫ FЈ x y 0 Ž .x5 5 5 FЈ y F L x y y . In this paper, we weaken this condition, assuming that 5 w Ž . Ž .x5 Ž5 5 . ⌫ FЈ x y FЈ x F x y x for a given

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## Detailed formulae for the convergence coeficients of the interval Newton iteration procedure are given. These are generaIized to iterations satisfJ>ing a weak nonsingular systems property.