On a theorem of L.V. Kantorovich concerning Newton's method
| Autor: | Ioannis K. Argyros |
|---|---|
| Rok vydání: | 2003 |
| Předmět: |
Kantorovich's convergence theorem
Banach space Numerical analysis Applied Mathematics Mathematical analysis Fréchet derivative symbols.namesake Local–semilocal convergence Computational Mathematics Operator (computer programming) Newton's method Newton fractal Radius of convergence Convergence (routing) symbols Applied mathematics Mathematics |
| Zdroj: | Journal of Computational and Applied Mathematics. 155(2):223-230 |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/s0377-0427(02)00865-8 |
| Popis: | We study the problem of approximating a locally unique solution of an operator equation using Newton's method. The well-known convergence theorem of L.V. Kantorovich involves a bound on the second Fréchet-derivative or the Lipschitz–Fréchet-differentiability of the operator involved on some neighborhood of the starting point. Here we provide local and semilocal convergence theorems for Newton's method assuming the Fréchet-differentiability only at a point which is a weaker assumption. A numerical example is provided to show that our result can apply to solve a scalar equation where the above-mentioned ones may not. |
| Databáze: | OpenAIRE |
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