In this paper, we discuss two variants of Newton's method without using any second derivative for solving nonlinear equations. By using the majorant function and confirming the majorant sequences, we obtain the cubic semilocal convergence and the error estimation in the Kantorovich-type theorems. Th
On the convergence of newton's method
β Scribed by Joel Friedman
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 803 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0885-064X
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π SIMILAR VOLUMES
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
A local convergence analysis of Newton's method for solving nonlinear equations, under a majorant condition, is presented in this paper. Without assuming convexity of the derivative of the majorant function, which relaxes the Lipschitz condition on the operator under consideration, convergence, the