논문KCI 등재
ON THE CONVERGENCE OF NEWTON'S METHOD ANDLOCALLY H？OLDERIAN OPERATORS
한국수학교육학회|2008.05|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제15권 제2호|pp. 111-120
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A semilocal convergence analysis is provided for Newton's method ina Banach space setting. The operators involved are only locally Holderian. We make use of a point-based approximation and center-Holderian hypotheses. This approach can be used to approximate solutions of equations involving nonsmooth operators.
Abstract
A semilocal convergence analysis is provided for Newton's method ina Banach space setting. The operators involved are only locally Holderian. We make use of a point-based approximation and center-Holderian hypotheses. This approach can be used to approximate solutions of equations involving nonsmooth operators.
참고문헌 (5)
- Argyros, I.K., "Advances in the Efficiency of Computational Methods and Applications" (2000), World Scientific Publ. Co.
- Argyros, I.K, "A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space", J. Math. Anal. and Applic, 298(2), pp.374~397 (2004)
- Kantorovich, L.V., "Functional Analysis in Normed Spaces" (1982), Pergamon Press
- Robinson, S.M., "An implicit function theorem for a class of nonsmooth functions", Mathematics of Operations Research, 16(2), pp.292~309 (1991)
- Robinson, S.M., "Newton's method for a class of nonsmooth functions", Set-Valued Analysis, 2, pp.291~305 (1994)
관련 논문AI추천
ON THE CONVERGENCE OF NEWTON'S METHOD AND LOCALLY HÖLDERIAN INVERSES OF OPERATORSIoannis K. Argyros한국수학교육학회 · 이론수학과 교직수학2009 · 제16권 제1호On the solution of nonlinear equations containing a non-differentiable termIoannis K. Argyros영남수학회 · East Asian Mathematical Journal2008 · 제24권 제3호CONVERGENCE THEOREMS FOR NEWTON'S AND MODIFIED NEWTON'S METHODSIoannis K. Argyros한국수학교육학회 · 이론수학과 교직수학2009 · 제16권 제4호On the convergence of Newton's method for set valued maps under weak conditionsIoannis K. Argyros강원경기수학회 · 한국수학논문집2012 · 제20권 제1호On the convergence of a Newton-like method under weak conditionsHongmin Ren, Ioannis K. Argyros대한수학회 · 대한수학회논문집2011 · 제26권 제4호APPROXIMATING SOLUTIONS OF EQUATIONSBY COMBINING NEWTON-LIKE METHODSIoannis K. Argyros한국수학교육학회 · 이론수학과 교직수학2008 · 제15권 제1호
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