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On the convergence of Newton's method for set valued maps under weak conditions

Ioannis K. Argyros
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2012.03|한국수학논문집 (Korean Journal of Mathematics)|제20권 제1호|pp. 117-123

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참고문헌

키워드

generalized equationsNewton’s methodSet valued mapsAubin continuitycenter-H¨older continuity.
주제분류수학

초록

We provide a convergence analysis of Newton’s method for set valued maps under center H¨older continuity conditions on the Fr´echet derivative of the operator involved. This approach extends the applicability of earlier works [4,5,7].

Abstract

We provide a convergence analysis of Newton’s method for set valued maps under center H¨older continuity conditions on the Fr´echet derivative of the operator involved. This approach extends the applicability of earlier works [4,5,7].

참고문헌 (8)

  1. I.K. Argyros, "The Newton–.Kantorovich method under mild differentiability conditions and the Ptak error estimates", Monatsh. Math, 101, pp.175~193 (1990)
  2. I.K. Argyros, "A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space", J. Math. Anal. Appl, 298, pp.374~397 (2004)
  3. I.K. Argyros, "Newton Methods" (2005), Nova Science Publ. Inc
  4. A.L. Dontchev, "Local convergence of the Newton method for generalized equations", C. R. Acad. Sci. Paris, S´er. I Math, 332, pp.327~331 (1996)
  5. A.L. Dontchev, "Uniform convergence of the Newton method for Aubin continuous maps", Serdica Math. J, 22, pp.385~398 (1996)
  6. A.D. Ioffe, "Theory of Extremal Problems" (1979), North Holland
  7. A. Pietrus, "Does Newton’s method for set-valued maps converge uniformly in mild differentiability context", Rev. Colombiana Mat, 30, pp.49~56 (2000)
  8. R.T. Rockafellar, "Lipschitz properties of multifunctions", Nonlinear Anal, 9, pp.867~885 (1985)

관련 논문AI추천

ON THE CONVERGENCE OF NEWTON'S METHOD ANDLOCALLY H？OLDERIAN OPERATORSIoannis K. Argyros한국수학교육학회 · 이론수학과 교직수학2008 · 제15권 제2호ON THE CONVERGENCE OF NEWTON'S METHOD AND LOCALLY HÖLDERIAN INVERSES OF OPERATORSIoannis K. Argyros한국수학교육학회 · 이론수학과 교직수학2009 · 제16권 제1호On the convergence of a Newton-like method under weak conditionsHongmin Ren, Ioannis K. Argyros대한수학회 · 대한수학회논문집2011 · 제26권 제4호Local convergence of Newton-like methods for generalized equationsIoannis K. Argyros영남수학회 · East Asian Mathematical Journal2009 · 제25권 제4호Improved convergence results for generalized equationsIoannis K. Argyros영남수학회 · East Asian Mathematical Journal2008 · 제24권 제2호On the solution of nonlinear equations containing a non-differentiable termIoannis K. Argyros영남수학회 · East Asian Mathematical Journal2008 · 제24권 제3호

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