LOCAL CONVERGENCE OF THE SECANT METHOD UPPER HOLDER CONTINUOUS DIVIDED DIFFERENCES
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The semilocal convergence of the secant method under Holder continuous divided di erences in a Banach space setting for solving nonlinear equations has been examined by us in [3]. The local convergence was recently examined in [4]. Motivated by optimization considerations and using the same hypotheses but more precise estimates than in [4] we provide a local convergence analysis with the following advantages: larger radius of convergence and ner error estimates on the distances involved. The results can be used for projection methods, to develop the cheapest possible mesh re nement strategies and to solve equations involving autonomous di erential equations [1], [4], [7], [8].
Abstract
The semilocal convergence of the secant method under Holder continuous divided di erences in a Banach space setting for solving nonlinear equations has been examined by us in [3]. The local convergence was recently examined in [4]. Motivated by optimization considerations and using the same hypotheses but more precise estimates than in [4] we provide a local convergence analysis with the following advantages: larger radius of convergence and ner error estimates on the distances involved. The results can be used for projection methods, to develop the cheapest possible mesh re nement strategies and to solve equations involving autonomous di erential equations [1], [4], [7], [8].
참고문헌 (8)
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