Convergence ball and error analysis of Ostrowski-Traub’s method

Convergence ball and error analysis of Ostrowski-Traub’s method

Under the hypotheses that the second-order and third-order derivatives of a function are bounded, an estimate of the radius of the convergence ball of Ostrowski-Traub’s method is obtained. An error analysis is given which matches the convergence order of the method. Finally, two examples are provide...

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Veröffentlicht in:Applied Mathematics-A Journal of Chinese Universities 2010-09, Vol.25 (3), p.374-378
Hauptverfasser: Bi, Wei-hong, Wu, Qing-biao, Ren, Hong-min
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Zusammenfassung:Under the hypotheses that the second-order and third-order derivatives of a function are bounded, an estimate of the radius of the convergence ball of Ostrowski-Traub’s method is obtained. An error analysis is given which matches the convergence order of the method. Finally, two examples are provided to show applications of our theorem.
ISSN:1005-1031
1993-0445
DOI:10.1007/s11766-010-2447-y