Advanced search
Publication Cover
International Journal of Computer Mathematics Volume 86, 2009 - Issue 3
Submit an article Journal homepage
81
Views
8
CrossRef citations to date
0
Altmetric
Section B

Convergence analysis for a deformed Newton's method with third-order in Banach space under γ-condition

Yueqing Zhao Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, People's Republic of China; Department of Mathematics, Taizhou University, Linhai, Zhejiang, People's Republic of China
&
Qingbiao Wu Department of Mathematics, Taizhou University, Linhai, Zhejiang, People's Republic of ChinaCorrespondence[email protected]
Pages 441-450 | Received 20 Jan 2006, Accepted 25 Jul 2007, Published online: 21 Feb 2009

References

  • Argyros , I. K. 1994 . On the midpoint iterative method for solving nonlinear operator equations and applications to the solution of integral equations . Rev. Anal. Numér Théor. Approx. , 23 : 139 – 152 .
  • Argyros , I. K. 1998 . Sufficient conditions for constructing methods faster than Newton's method . Appl. Math. Comput. , 93 : 169 – 181 .
  • Argyros , I. K. 2003 . On a theorem of L.V. Kantorovich concerning Newton's method . J. Comput. Appl. Math. , 155 : 223 – 230 .
  • Argyros , I. K. 2004 . On the Newton–Kantorovich hypothesis for solving equations . J. Comput. Appl. Math. , 169 : 315 – 332 .
  • Chen , D. and Argyros , I. K. 1992 . On the midpoint method for solving equations in Banach spaces . Appl. Math. Lett. , 5 : 7 – 9 .
  • Frontini , M. and Sormani , E. 2003 . Some variant of Newton's method with third-order convergence . Appl. Math. Comput. , 140 : 419 – 426 .
  • Frontini , M. and Sormani , E. 2003 . Modified Newton's method with third-order convergence and multiple roots . J. Comput. Appl. Math. , 156 : 345 – 354 .
  • Frontini , M. and Sormani , E. 2004 . Third-order methods from quadrature formulae for solving systems of nonlinear equations . Appl. Math. Comput. , 149 : 771 – 782 .
  • Hernandez , M. A. 2001 . A modification of the classical Kantorovich conditions for Newton's method . J. Comput. Appl. Math. , 137 : 201 – 205 .
  • Homeier , H. H.H. 2003 . A modified Newton method for root finding with cubic convergence . J. Comput. Appl. Math. , 157 : 227 – 230 .
  • Homeier , H. H.H. 2004 . A modified Newton method with cubic convergence: The multivariate case . J. Comput. Appl. Math. , 169 : 161 – 169 .
  • Huang , Z. D. 1993 . A note on the Kantorovich theorem for Newton iteration . J. Comput. Appl. Math. , 47 : 211 – 217 .
  • Kantorovich , L. 1949 . On Newton method (Russian) . Tr. Mat. Inst. Steklov. , 28 : 104 – 144 .
  • Kou , J. S. , Li , Y. T. and Wang , X. H. 2006 . On modified Newton methods with cubic convergence . Appl. Math. Comput. , 176 : 123 – 127 .
  • Kou , J. S. , Li , Y. T. and Wang , X. H. 2006 . A modification of Newton method with third-order convergence . Appl. Math. Comput. , 181 : 1106 – 1111 .
  • Ortega , J. M. and Rheinbolt , W. C. 1970 . Iterative solution of nonlinear equations in several variables , New York : Academic Press .
  • Wang , X. H. 1997 . Convergence on the iteration of Halley family in weak condition . Chinese Sci. Bull. , 42 : 552 – 555 .
  • Wang , X. H. 2003 . Convergence of Newton's method and and uniqueness of the solution of equations in Banach spaces II . Acta Math. Sinica, English Series. , 19 : 405 – 412 .
  • Weerakoon , S. and Fernando , T. G.I. 2000 . A variant of Newton's method with accelerated third-order convergence . Appl. Math. Lett. , 13 : 87 – 93 .
  • Wu , Q. B. and Zhao , Y. Q. 2006 . Third-order convergence theorem by using majorizing function for a modified Newton method in Banach space . Appl. Math. Comput. , 175 : 1515 – 1524 .

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:

Order Reprints Request Corporate Permissions

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:

Request Academic Permissions

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.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.