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LOCAL RESULTS FOR A CONTINUOUS ANALOG OF NEWTON'S METHOD

Ioannis K. Argyros|Said Hilout
영남수학회 (Youngnam Mathematical Society)|2010.05|East Asian Mathematical Journal|제26권 제3호|pp. 365-370

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참고문헌

키워드

Hilbert spacecontinuous Newton's methodradius of conver-genceLipschitz condition
주제분류수학

초록

A local convergence result is provided for the continuous analog of Newton's method in a Banach space setting. The radius of convergence is larger, the error bounds tighter, and under the same or weaker hypotheses than before [12].

Abstract

A local convergence result is provided for the continuous analog of Newton's method in a Banach space setting. The radius of convergence is larger, the error bounds tighter, and under the same or weaker hypotheses than before [12].

참고문헌 (15)

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  2. R. G. Airapetyan, "Dynamical systems and discrete methods for solving nonlinear ill{posed problems", pp.491~536 (2000), World Publishers
  3. R. G. Airapetyan, "Continuous analog of Gauss-Newton method", Math. Models Methods Appl. Sci., 9, pp.463~474 (1999)
  4. R. G. Airapetyan, "Continuous method for solving nonlinear ill{posed problems", Amer. Math. Soc., Providence RI, Fields. Inst. Commun, 25, pp.111~137 (2000)
  5. I. K. Argyros, "On the Newton{Kantorovich hypothesis for solving equations", J. Comput. Appl. Math., 169, pp.315~332 (2004)
  6. 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)
  7. I. K. Argyros, "Computational theory of iterative methods, Series: Studies in Computational Mathematics 15" (2007), Elsevier Publ. Co.
  8. R. Courant, "Variational methods for the solution of problems of equilibrium and vibra- tions", Bull. Amer. Math. Soc., 49, pp.1~23 (1943)
  9. M. K. Gavurin, "Nonlinear functional equations and continuous analogs of iterative meth- ods", Izv. Vuzov. Ser. Matematika, 5, pp.18~31 (1958)
  10. B. Kaltenbacher, "On Broyden's method for the regularization of nonlinear ill{posed problems", Numer. Funct. Anal. Optimiz., 19, pp.807~833 (1998)
  11. A. G. Ramm, "Linear ill{posed problems and dynamical systems", J. Math. Anal. Appl., 258, pp.448~456 (2001)
  12. A. G. Ramm, "Acceleration of convergence of a continuous analog of the Newton method", Appl. Anal., 81, pp.1001~1004 (2002)
  13. A. G. Ramm, "Dynamical systems method for solving operator equations", Commun. Nonlinear. Sci. Numer. Simul., 9, pp.383~402 (2004)
  14. A. G. Ramm, "Continuous regularized Gauss{Newton{type algorithm for nonlinear ill{posed equations with simultaneous updates of inverse derivative", Int. J. Pure. Appl. Math., 2, pp.23~34 (2002)
  15. A. G. Ramm, "Continuous modied Newton's{type method for nonlinear operator equations", Annali di Matematica, 182, pp.37~52 (2003)

관련 논문AI추천

ON THE CONVERGENCE OF NEWTON'S METHOD ANDLOCALLY H？OLDERIAN OPERATORSIoannis K. Argyros한국수학교육학회 · 이론수학과 교직수학2008 · 제15권 제2호CONVERGENCE THEOREMS FOR NEWTON'S AND MODIFIED NEWTON'S METHODSIoannis K. Argyros한국수학교육학회 · 이론수학과 교직수학2009 · 제16권 제4호ON THE CONVERGENCE OF NEWTON'S METHOD AND LOCALLY HÖLDERIAN INVERSES OF OPERATORSIoannis K. Argyros한국수학교육학회 · 이론수학과 교직수학2009 · 제16권 제1호ON THE RADIUS OF CONVERGENCE OF SOME NEWTON{TYPE METHODS IN BANACH SPACESIoannis K. Argyros, Said Hilout한국수학교육학회 · 이론수학과 교직수학2011 · 제18권 제3호CONCERNING THE RADII OF CONVERGENCE FOR ACERTAIN CLASS OF NEWTON-LIKE METHODSIoannis K. Argyros한국수학교육학회 · 이론수학과 교직수학2008 · 제15권 제1호Local convergence of Newton-like methods for generalized equationsIoannis K. Argyros영남수학회 · East Asian Mathematical Journal2009 · 제25권 제4호

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