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A semilocal convergence analysis for a certain class of modified Newton processes

Ioannis K. Argyros
영남수학회 (Youngnam Mathematical Society)|2008.03|East Asian Mathematical Journal|제24권 제2호|pp. 151-159

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참고문헌

키워드

Banach spaceNewton’s methodsemilocal convergenceFr´echet derivativeNondiscrete Mathematical Induction
주제분류수학

초록

An error analysis introduced in [1], [2] is utilized in combination with nondiscrete mathematical induction to provide a finer than before [3]–[7], [11] semilocal convergence analysis for a certain class of modified Newton processes.

Abstract

An error analysis introduced in [1], [2] is utilized in combination with nondiscrete mathematical induction to provide a finer than before [3]–[7], [11] semilocal convergence analysis for a certain class of modified Newton processes.

참고문헌 (12)

  1. Argyros, I. K., "unifying local-semilocal convergence analysis and applications for two-point Newton like methods in Banach space", J. Math. Anal. Applic, 298, pp.374~397 (2004)
  2. Argyros, I. K., "Approximate Solution of Operator Equations with Applications" (2005), World Scientific Publ. Co.
  3. Dennis, J, "On the Kantorovich hypothesis for Newton’s method", SIAM J. Numer. Anal, 6, pp.493~507 (1969)
  4. Kantorovich, L.V., "Functional Analysis in Normed Spaces" (1982), Pergamon Press
  5. Nastas, N.K., "The convergence of a certain third order process for the solution of non- linear operator equations", Approximate Solution of Equations, “Stiinca” Kishinev, 70~75 (1973)
  6. Potra, F.A., "Sharp error bounds for Newton’s method", Numer. Math, 34, pp.63~72 (1980)
  7. Potra, F.A., "On a class of modified Newton processes", Numer. Funct. Anal. and Optimiz, 1, pp.107~120 (1980)
  8. Potra, F.A., "Nondiscrete Induction and Iterative Processes" (1984), Pitman Publ.
  9. Ptak, V., "Nondiscrete mathematical induction and iterative existence proofs", Linear Algebra and its Applications, 13, pp.223~236 (1976)
  10. Ptak, V., "The rate of convergence of Newton’s process", Numer. Math, 25, pp.279~285 (1976)
  11. chmidt, J.W., "Ableitungsfreie Verfahren mit h¨oherer Konvergenzge schwindigkeit", Computing, 3, pp.215~226 (1968)
  12. Yamamoto, T., "A method for finding sharp error bounds for Newton’s method under the Kantorovich assumptions", Numer. Math, 44, pp.203~220 (1986)

관련 논문AI추천

Improved local convergence analysis for a three point method of convergence order 1.839$\dots$조열제, Ioannis K. Argyros, Santhosh George대한수학회 · 대한수학회보2019 · 제56권 제3호CONCERNING THE RADII OF CONVERGENCE FOR ACERTAIN CLASS OF NEWTON-LIKE METHODSIoannis K. Argyros한국수학교육학회 · 이론수학과 교직수학2008 · 제15권 제1호On the convergence of a Newton-like method under weak conditionsHongmin Ren, Ioannis K. Argyros대한수학회 · 대한수학회논문집2011 · 제26권 제4호A UNIFIED CONVERGENCE ANALYSIS FOR SECANT-TYPE METHODSAngel Alberto Magrenan, Ioannis Konstantinos Argyros대한수학회 · 대한수학회지2014 · 제51권 제6호ON THE SEMILOCAL CONVERGENCE OF A NEWTON-TYPE METHOD OF ORDER THREEIoannis K. Argyros, Said Hilout한국수학교육학회 · 이론수학과 교직수학2010 · 제17권 제1호IMPROVED CONVERGENCE OF STEFFENSEN’S METHOD FOR APPROXIMATING FIXED POINTS OF OPERATORS IN BANACH SPACEHongmin Ren, Ioannis K. Argyros대한수학회 · 대한수학회지2017 · 제54권 제1호

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