Under weak conditions, we present an iteration formula to improve Newton's method for solving nonlinear equations. The method is free from second derivatives, permitting f (x) = 0 in some points and per iteration it requires two evaluations of the given function and one evaluation of its derivative.
Weak sufficient convergence conditions and applications for newton methods
β Scribed by Ioannis K. Argyros
- Publisher
- Springer-Verlag
- Year
- 2004
- Tongue
- English
- Weight
- 177 KB
- Volume
- 16
- Category
- Article
- ISSN
- 1598-5865
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let X 1 ; : : : ; X n be a sequence of i.i.d. random variables with common distribution P on the real line. Assuming that P has a smooth density, we construct a histogram based estimator P n; H and establish weak convergence of the empirical process β n(P n; H -P)(f) fβF under sharp conditions. If
The classical Kantorovich theorem on Newton's method assumes that the first 5 w Ε½ . derivative of the operator involved satisfies a Lipschitz condition β« FΠ x y 0 Ε½ .x5 5 5 FΠ y F L x y y . In this paper, we weaken this condition, assuming that 5 w Ε½ . Ε½ .x5 Ε½5 5 . β« FΠ x y FΠ x F x y x for a given