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We present a local convergence analysis of some Newton-like methods of R-order at least three in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second $Fr{\acute{e}}chet$-derivative of the operator involved. These conditions are weaker that the corresponding ones given by Hernandez, Romero [10] and others [1], [4]-[9] requiring hypotheses up to the third $Fr{\acute{e}}chet$ derivative. Numerical examples are also provided in this study.
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참고문헌 (13)
참고문헌 신청
S. Amat / 2008 / A modiffed Chebyshev's iterative method with at least sixth order of convergence / Appl. Math. Comput 206(1):164~174
I. K. Argyros / 2008 / Convergence and Application of Newton-type Iterations / Springer
I. K. Argyros / 2010 / A convergence analysis for directional two-step Newton methods / Numer. Algor 55:503~528
V. Candela / 1990 / Recurrence relations for rational cubic methods I: The Halley method / Computing 44:169~184
V. Candela / 1990 / Recurrence relations for rational cubic methods II: The Chebyshev method / Computing 45(4):355~367
I. K. Argyros / 2008 / Convergence and Application of Newton-type Iterations / Springer
I. K. Argyros / 2010 / A convergence analysis for directional two-step Newton methods / Numer. Algor 55:503~528
V. Candela / 1990 / Recurrence relations for rational cubic methods I: The Halley method / Computing 44:169~184
V. Candela / 1990 / Recurrence relations for rational cubic methods II: The Chebyshev method / Computing 45(4):355~367
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