본문 바로가기
KERD
논문KCI 등재

On the convergence of a Newton-like method under weak conditions

Ioannis K. Argyros|Hongmin Ren
대한수학회 (The Korean Mathematical Society)|2011.10|대한수학회논문집 (Communications of the KMS)|제26권 제4호|pp. 575-584

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

semilocal convergenceNewton-like methodBanach space settingGateaux-derivativehemicontinuity
주제분류수학

초록

We provide a semilocal convergence analysis for a Newton-like method under weak conditions in a Banach space setting. In particular, we only assume that the Gateaux derivative of the operator involved is hemicontinuous. An application is also provided.

Abstract

We provide a semilocal convergence analysis for a Newton-like method under weak conditions in a Banach space setting. In particular, we only assume that the Gateaux derivative of the operator involved is hemicontinuous. An application is also provided.

참고문헌 (12)

  1. I. K. Argyros, "Convergence theorems for Newton-like methods without Lipschitz condi- tions", Comm. Appl. Nonlinear Anal, 9(3), pp.103~111 (2002)
  2. I. K. Argyros, "On a theorem of L. V. Kantorovich concerning Newton's method", J. Comput. Appl. Math, 155(2), pp.223~230 (2003)
  3. I. K. Argyros, "Unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space", J. Math. Anal. Appl, 298(2), pp.374~397 (2004)
  4. I. K. Argyros, "Computational theory of iterative methods, Studies in Computational Mathe- matics" (2007), 15. Elsevier B. V
  5. E. Catinas, "On some iterative methods for solving nonlinear equations", Rev. Anal. Numer. Theor. Approx, 23(1), pp.47~53 (1994)
  6. X. Chen, "Convergence domains of certain iterative methods for solv- ing nonlinear equations", Numer. Funct. Anal. Optim, 10(1), pp.37~48 (1989)
  7. W. B. Johnson, "Handbook of the Geometry of Banach Spaces", Elsevier, Science B.V, 2 (2003)
  8. L. V. Kantorovich, "Functional Analysis in Normed Spaces" (1982), Pergamon Press
  9. P. D. Proinov, "New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems", J. Complexity, 26(1), pp.3~42 (2010)
  10. M. M. Vainberg, "Variational Methods for the Study of Nonlinear Operators" (1964), Holden Day Inc
  11. P. P. Zabrejko, "The majorant method in the theory of Newton- Kantorovich approximations and the Ptak error estimates", Numer. Funct. Anal. Optim, 9(5), pp.671~684 (1987)
  12. A. I. Zincenko, "Some approximate methods of solving equations with non-differentiable operators, Dopovidi Akad", Nauk Ukrain. RSR, 1963, pp.156~161 (1963)

관련 논문AI추천

ON THE CONVERGENCE OF NEWTON'S METHOD AND LOCALLY HÖLDERIAN INVERSES OF OPERATORSIoannis K. Argyros한국수학교육학회 · 이론수학과 교직수학2009 · 제16권 제1호ON THE CONVERGENCE OF NEWTON'S METHOD ANDLOCALLY H？OLDERIAN OPERATORSIoannis K. Argyros한국수학교육학회 · 이론수학과 교직수학2008 · 제15권 제2호Local convergence of Newton-like methods for generalized equationsIoannis K. Argyros영남수학회 · East Asian Mathematical Journal2009 · 제25권 제4호APPROXIMATING SOLUTIONS OF EQUATIONSBY COMBINING NEWTON-LIKE METHODSIoannis K. Argyros한국수학교육학회 · 이론수학과 교직수학2008 · 제15권 제1호Enlarging the ball of convergence of secant-like methods for non-differentiable operatorsHongmin Ren, IOANNISK.ARGYROS대한수학회 · 대한수학회지2018 · 제55권 제1호Improved convergence results for generalized equationsIoannis K. Argyros영남수학회 · East Asian Mathematical Journal2008 · 제24권 제2호

이 간행물의 다른 논문 (16건)

Bipolar fuzzy a-ideals of BCI-algebras전영배, 이경자pp. 531-542Free algebras over a poset in varietiesAldo Figallo, Jr., Alicia Zilianipp. 543-549A short proof of an identity for cubic partition functionXinhua Xiongpp. 551-555Quasi-Armendariz property for skew polynomial ringsMuhittin Ba(특수문자)er, 곽태근pp. 557-573Jordan (φ, ψ)-derivations in JB^*-triplesAbbas Najati, Mohammad Sal Moslehianpp. 585-589
원문 보기