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LOCAL CONVERGENCE OF THE GAUSS-NEWTON METHOD FOR INJECTIVE-OVERDETERMINED SYSTEMS

Sergio Amat|Ioannis Konstantinos Argyros|Ángel Alberto Magreñán
대한수학회 (The Korean Mathematical Society)|2014.09|대한수학회지 (Journal of the KMS)|제51권 제5호|pp. 955-970

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참고문헌

키워드

Hilbert spaceslocal convergenceradius of convergencethe Gauss-Newton methodmajorant conditioninjective-overdetermined systems.
주제분류수학

초록

We present, under a weak majorant condition, a local conver- gence analysis for the Gauss-Newton method for injective-overdetermined systems of equations in a Hilbert space setting. Our results provide un- der the same information a larger radius of convergence and tighter er- ror estimates on the distances involved than in earlier studies such us [10, 11, 13, 14, 18]. Special cases and numerical examples are also in- cluded in this study.

Abstract

We present, under a weak majorant condition, a local conver- gence analysis for the Gauss-Newton method for injective-overdetermined systems of equations in a Hilbert space setting. Our results provide un- der the same information a larger radius of convergence and tighter er- ror estimates on the distances involved than in earlier studies such us [10, 11, 13, 14, 18]. Special cases and numerical examples are also in- cluded in this study.

참고문헌 (22)

  1. S. Amat, "Geometric constructions of iterative functions to solve nonlinear equations", J. Comput. Appl. Math, 157(1), pp.197~205 (2003)
  2. J. Appel, "New results on Newton-Kantorovich approximations with applications to nonlinear integral equations", Numer. Funct. Anal. Optimiz, 18(1-2), pp.1~17 (1997)
  3. I. K. Argyros, "Computational Theory of Iterative Methods" (2007), Elsevier
  4. I. K. Argyros, "Concerning the semilocal convergence of Newton's method and convex majorants", Rend. Circ. Mat. Palermo (2), 57(3), pp.331~341 (2008)
  5. I. K. Argyros, "Concerning the convergence of Newton's method and quadratic majorants", J. Appl. Math. Comput, 29(1-2), pp.391~400 (2009)
  6. I. K. Argyros, "A semilocal convergence analysis for directional Newton methods", Math. Comp, 80(273), pp.327~343 (2011)
  7. I. K. Argyros, "Extending the applicability of the Gauss-Newton method under average Lipschitz-conditions", Numer. Algorithms, 58(1), pp.23~52 (2011)
  8. I. K. Argyros, "Improved local convergence of Newton's method under weak majorant condition", J. Comput. Appl. Math, 236(7), pp.1892~1902 (2012)
  9. I. K. Argyros, "Computational Methods in Nonlinear Analysis" (2013), World Scientific Publ. Comp.
  10. O. P. Ferreira, "Local convergence of Newton's method in Banach space from the viewpoint of the majorant principle", IMA J. Numer. Anal, 29(3), pp.746~759 (2009)
  11. O. P. Ferreira, "Local convergence of Newton's method under majorant condition", J. Comput. Appl. Math, 235(5), pp.1515~1522 (2011)
  12. O. P. Ferreira, "Local convergence analysis of the Gauss-Newton method under a majorant condition", J. Complexity, 27(1), pp.111~125 (2011)
  13. O. P. Ferreira, "Kantorovich's majorants principle for Newton's method", Comput. Optim. Appl, 42(2), pp.213~229 (2009)
  14. M. L. N. Goncalves, "Local convergence of the Gauss-Newton method for injective-overdetermined systems of equations under a majorant condition", Comput. Math. Appl, 66(4), pp.490~499 (2013)
  15. J. M. Gutierrez, "Accessibility of solutions by Newton's method", Inter. J. Comput. Math, 57(3-4), pp.239~247 (1995)
  16. W. M. A. Haussler, "Kantorovich-type convergence analysis for the Gauss-Newton method", Numer. Math, 48(1), pp.119~125 (1986)
  17. L. V. Kantorovich, "Functional Analysis in Normed Spaces" (1964), Pergamon Press
  18. C. Li and, "Majorizing functions and convergence of the Gauss-Newton method for convex composite optimization", SIAM J. Optim, 18(2), pp.613~692 (2007)
  19. A. A. Magrenan, "Estudio de la dinamica del metodo de Newton amortiguado", PhD, pp.2013
  20. P. D. Proinov, "General local convergence theory for a class of iterative processes and its applications to Newton's method", J. Complexity, 25(1), pp.38~62 (2009)
  21. W. C. Rheinboldt, "An adaptive continuation process for solving systems of nonlinear equations", Banach Ctr. Publ, 3(1), pp.129~142 (1977), Polish Academy of Science
  22. X. Wang, "Convergence on Newton's method and inverse function theorem in Banach space", Math. Comput, 68(225), pp.169~186 (1999)

관련 논문AI추천

Extending the applicability of inexact Gauss--Newton method for solving underdetermined nonlinear least squares problemsGilson do Nascimento Silva, Ioannis Konstantinos Argyros대한수학회 · 대한수학회지2019 · 제56권 제2호ON THE SEMILOCAL CONVERGENCE OF THE GAUSS-NEWTON METHOD USING RECURRENT FUNCTIONSIoannis K. Argyros, Said Hilout한국수학교육학회 · 이론수학과 교직수학2010 · 제17권 제4호Local convergence of Newton-like methods for generalized equationsIoannis K. Argyros영남수학회 · East Asian Mathematical Journal2009 · 제25권 제4호CONVERGENCE THEOREMS FOR NEWTON'S AND MODIFIED NEWTON'S METHODSIoannis K. Argyros한국수학교육학회 · 이론수학과 교직수학2009 · 제16권 제4호SEMILOCAL CONVERGENCE OF NEWTON’S METHOD FOR SINGULAR SYSTEMS WITH CONSTANT RANK DERIVATIVESIoannis K. Argyros, Said Hilout한국수학교육학회 · 이론수학과 교직수학2011 · 제18권 제2호On the convergence of a Newton-like method under weak conditionsHongmin Ren, Ioannis K. Argyros대한수학회 · 대한수학회논문집2011 · 제26권 제4호

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