112
Views
6
CrossRef citations to date
0
Altmetric
Section B

On local convergence of a Newton-type method in Banach space

&
Pages 1366-1374 | Received 20 Apr 2007, Accepted 30 Nov 2007, Published online: 17 Jun 2009

References

  • Amat , S. 2004 . A fast Chebyshev's method for quadratic equations . Appl. Math. Comput. , 148 : 461 – 474 .
  • Argyros , I. K. 2004 . A unifying local-semilocal convergence analysis and application for two-point Newton-like methods in Banach space . J. Math. Anal. Appl. , 298 : 374 – 397 .
  • Argyros , I. K. 2005 . Concerning the “terra incognita” between convergence regions of two Newton methods . Nonlinear Anal. , 62 : 179 – 194 .
  • Argyros , I. K. 2007 . “ Computational theory of iterative methods, injStudies in Computational Mathematics ” . Edited by: Chui , C. K. and Wuytack , L. Vol. 15 , New York, , USA : Elsevier Science Inc .
  • Argyros , I. K. and Chen , D. 1992 . On the midpoint iterative method for solving nonlinear equations in Banach spaces . Appl. Math. Lett. , 5 : 7 – 9 .
  • Chen , J. and Shen , Z. 2007 . Convergence analysis of the secant type methods . Appl. Math. Comput. , 188 : 514 – 524 .
  • Gutierrez , J. M. and Hernández , M. A. 2001 . An acceleration of Newton's method: Super-Halley method . Appl. Math. Comput. , 117 : 223 – 239 .
  • Hernández , M. A. and Salanova , M. A. 2000 . Modification of the Kantorovich assumptions for semilocal convergence of the Chebyshev method . J. Comput. Appl. Math. , 126 : 131 – 143 .
  • Homeier , H. H.H. 2003 . A modified Newton method for rootfinding with cubic convergence . J. Comput. Appl. Math. , 157 : 227 – 230 .
  • Huang , Z. 2004 . The convergence ball of Newton's method and uniqueness ball of the of equations under Hölder-type continuous derivatives . Comput. Math. Appl. , 47 : 247 – 251 .
  • Kantorovich , L. V. and Akilov , G. P. 1982 . Functional Analysis , 2 , Oxford : Pergamon Press .
  • Ortega , J. M. and Rheinboldt , W. C. 1970 . Iterative Solution of Nonlinear Equations in Several Variables , New York : Academic Press .
  • Özban , A. Y. 2004 . Some new variants of Newton's method . Appl. Math. Lett. , 17 : 677 – 682 .
  • Ren , H. M. 2006 . On the local convergence of a deformed Newton's method under Argyros-type condition . J. Math. Anal. Appl. , 321 : 396 – 404 .
  • Ren , H. M. and Wu , Q. B. 2006 . The convergence ball of the Secant method under Hölder continuous divided differences . J. Comput. Appl. Math. , 194 : 284 – 293 .
  • Traub , J. F. and Wozniakowski , H. 1979 . Convergence and complexity of Newton iteration . J. Assoc. Comput. Math. , 29 : 250 – 258 .
  • Wang , X. 1980 . The convergence on Newton's method, Kexue Tongbao (A Special Issue of Mathematics, Physics & Chemistry) , 25 : 36 – 37 .
  • Wang , X. 1999 . Convergence of Newton's method and inverse function in Banach space . Math. Comput. , 68 : 169 – 186 .
  • Wang , X. 2000 . Convergence of Newton's method and uniqueness of the solution of equations in Banach space . IMA J. Numer. Anal. , 20 : 123 – 134 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.