15
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Improved error bounds for the modified secant method

Pages 99-109 | Received 10 Jun 1991, Published online: 19 Mar 2007

References

  • Argyros , I. K. 1987 . Newton-like methods under mild differentiability conditions with error analysis . Bull. Austral. Math. Soc. , 37 ( 2 ) : 131 – 147 .
  • Argyros , I. K. 1988 . On Newton's method and nondiscrete mathematical induction . Bull. Austral. Math. Soc. , 38 ( 2 ) : 131 – 140 .
  • Dennis , J. E. 1971 . “ Toward a unified convergence theory for Newton-like methods ” . In Nonlinear Functional Analysis and Applications , Edited by: Rall , L. B. New York : Academic Press .
  • Gragg , W. B. and Tapia , R. A. 1974 . Optimal error bounds for the Newton-Kantorovich theorem . SIAM J. Numer. Anal. , 11 ( 1 ) : 10 – 13 .
  • Ostrowski , M. A. 1973 . Solution of equations in Euclidian and Banach spaces , New York : Academic Press .
  • Potra , F. A. 1980 . Sharp error bounds for Newton's process . Numer. Math. , 34 : 63 – 72 .
  • Potra , F. A. 1982 . An error analysis for the Secant method . Numer. Math. , 32 : 427 – 445 .
  • Potra , F. A. 1985 . Sharp error bounds for a class of Newton-like methods . Libertas Mathematica , 5 : 71 – 84 .
  • Potra , F. A. and Ptâk , V. 1984 . Nondiscrete induction and iterative processes , Boston : Pitman Publ. .
  • Ptâk , V. 1976 . Nondiscrete mathematical induction and iterative existence proofs . Linear Algebra Appl. , 13 : 223 – 236 .
  • Schmidt , J. W. 1974 . Regula-Falsi Verfahren ml2 Konsistenter Steigung und Majoranten Prinzip . Period. Math. Hungar. , 5 ( 3 ) : 187 – 193 .
  • Sergeev , A. A. 1961 . On the method of chords Sibirsk . Mat. Z. , 2 ( 3 ) : 282 – 289 .
  • Ulm , S. 1964 . Majorant principle and the Secant method (in Russian), I.A.N. Estonskoi S.S.R . fiz. mat. , 3 ( 3 ) : 217 – 227 .
  • Yamamoto , T. 1987 . A convergence theorem for Newton-like methods in Banach spaces . Numer. Math. , 51 ( 3 ) : 545 – 557 .

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.