- Tytuł:
- The effect of rounding errors on a certain class of iterative methods
- Autorzy:
- Argyros, Ioannis
- Powiązania:
- https://bibliotekanauki.pl/articles/1208172.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Fréchet derivative
Lipschitz conditions
Newton-like method
inexact Newton-like method
Banach space - Opis:
- In this study we are concerned with the problem of approximating a solution of a nonlinear equation in Banach space using Newton-like methods. Due to rounding errors the sequence of iterates generated on a computer differs from the sequence produced in theory. Using Lipschitz-type hypotheses on the mth Fréchet derivative (m ≥ 2 an integer) instead of the first one, we provide sufficient convergence conditions for the inexact Newton-like method that is actually generated on the computer. Moreover, we show that the ratio of convergence improves under our conditions. Furthermore, we provide a wider choice of initial guesses than before. Finally, a numerical example is provided to show that our results compare favorably with earlier ones.
- Źródło:
-
Applicationes Mathematicae; 2000, 27, 3; 369-375
1233-7234 - Pojawia się w:
- Applicationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł