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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2008.1
- 수록면
- 295 - 304 (10page)
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초록· 키워드
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We approximate a locally unique solution of a nonlinear operator equation containing a non-differentiable operator in a Banach space setting using Newton's method. Sufficient conditions for the semilocal convergence of Newton's method in this case have been given by several authors using mainly increasing sequences [1]-[6]. Here, we use center as well as Lipschitz conditions and decreasing majorizing sequences to obtain new sufficient convergence conditions weaker than before in many interesting cases. Numerical examples where our results apply to solve equations but earlier ones cannot [2], [5], [6] are also provided in this study.
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참고문헌 (6)
참고문헌 신청
I.K. Argyros / 1990 / On the solution of equations with non dierentiable operators and the Ptak error estimates / BIT 30 : 725 ~ 754
I.K. Argyros / 2004 / A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space / J. Math. Anal. and Appl 298 : 374 ~
I.K. Argyros / 2007 / Computational theory of iterative methods / Elsevier
J. Appel / 1995 / On the two-step Newton method for the solution of nonlinear operator equations / Math. Nachr 172 : 5 ~ 14
P.P. Zabrejko / 1985 / Generalization of the Newton-Kantorovich method for an equation with non-dierentiable operator (Russian) / Ukr. Mat. Zhurn 34 : 365 ~ 369
I.K. Argyros / 2004 / A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space / J. Math. Anal. and Appl 298 : 374 ~
I.K. Argyros / 2007 / Computational theory of iterative methods / Elsevier
J. Appel / 1995 / On the two-step Newton method for the solution of nonlinear operator equations / Math. Nachr 172 : 5 ~ 14
P.P. Zabrejko / 1985 / Generalization of the Newton-Kantorovich method for an equation with non-dierentiable operator (Russian) / Ukr. Mat. Zhurn 34 : 365 ~ 369
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