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We present a new local as well as a semilocal convergence analysis for Steffensen's method in order to locate fixed points of operators on a Banach space setting. Using more precise majorizing sequences we show under the same or less computational cost that our convergence criteria can be weaker than in earlier studies such as \cite{1,2,3,4,5,6,7,8,9,10,11,12,13}, \cite{21,22}. Numerical examples are provided to illustrate the theoretical results.
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참고문헌 (27)
참고문헌 신청
A. A. Magrenan / 2014 / A new tool to study real dynamics: The convergence plane / Appl. Math. Comput 248 : 215 ~ 224
A. Cordero / 2013 / Increasing the order of convergence of iterative schemes for solving nonlinear systems / J. Comput. Appl. Math 253 : 86 ~ 94
B. A. Bel’tjukov / 1965 / On a certain method of solution of nonlinear functional equations / Z. Vycisl. Mat. i Mat. Fiz 5 : 927 ~ 931
I. K. Argyros / 1996 / An error analysis for the Steffensen method under generalized Zabrejko-Nguen-type assumptions / Rev. Anal. Numer. Theor. Approx 25 (1-2) : 11 ~ 22
I. K. Argyros / 2000 / On the convergence of Steffensen-Galerkin methods / Atti Sem. Mat. Fis. Univ. Modena 48 (2) : 355 ~ 370
A. Cordero / 2013 / Increasing the order of convergence of iterative schemes for solving nonlinear systems / J. Comput. Appl. Math 253 : 86 ~ 94
B. A. Bel’tjukov / 1965 / On a certain method of solution of nonlinear functional equations / Z. Vycisl. Mat. i Mat. Fiz 5 : 927 ~ 931
I. K. Argyros / 1996 / An error analysis for the Steffensen method under generalized Zabrejko-Nguen-type assumptions / Rev. Anal. Numer. Theor. Approx 25 (1-2) : 11 ~ 22
I. K. Argyros / 2000 / On the convergence of Steffensen-Galerkin methods / Atti Sem. Mat. Fis. Univ. Modena 48 (2) : 355 ~ 370
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