Error bounds for the secant method

Ioannis K. Argyros

Mathematica Slovaca (1991)

  • Volume: 41, Issue: 1, page 69-82
  • ISSN: 0139-9918

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Argyros, Ioannis K.. "Error bounds for the secant method." Mathematica Slovaca 41.1 (1991): 69-82. <http://eudml.org/doc/31513>.

@article{Argyros1991,
author = {Argyros, Ioannis K.},
journal = {Mathematica Slovaca},
keywords = {regula falsi; method of chords; method of nondiscrete mathematical induction; secant method; Banach spaces; error estimates},
language = {eng},
number = {1},
pages = {69-82},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Error bounds for the secant method},
url = {http://eudml.org/doc/31513},
volume = {41},
year = {1991},
}

TY - JOUR
AU - Argyros, Ioannis K.
TI - Error bounds for the secant method
JO - Mathematica Slovaca
PY - 1991
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 41
IS - 1
SP - 69
EP - 82
LA - eng
KW - regula falsi; method of chords; method of nondiscrete mathematical induction; secant method; Banach spaces; error estimates
UR - http://eudml.org/doc/31513
ER -

References

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  1. ARGYROS I. K., Newton-like methods under mild differentiability conditions with error analysis, Bull. Austral. Math. Soc. Vol. 37, 2, 1987, 131-147. (1987) MR0926985
  2. ARGYROS I. K., On Newton's method and nondiscrete mathematical induction, Bull. Austral. Math. Soc. Vol. 38, 1988, 131-140. (1988) Zbl0642.65043MR0968237
  3. DENNIS J. E., Toward a unified convergence theory for Newton-like methods, In: Nonlinear Functional Analysis and Applications, L. B. Rail, Ed., Academic Press, New York, 1971. (1971) Zbl0276.65029MR0278556
  4. GRAGG W. B., TAPIA R. A., Optimal error bounds for the Newton-Kantorovich theorem, S.I.A.M. J. Numer. Anal. 11, 1, 1974, 10-13. (1974) Zbl0284.65042MR0343594
  5. OSTROWSKI M. A., Solution of equations in Euclidian and Banach spaces, Academic Press, New York, 1973. (1973) MR0359306
  6. POTRA F. A., PTÁK V., Sharp error bounds for Newton's process, Numer. Math. 34, 1980, 63-72. (1980) Zbl0434.65034MR0560794
  7. POTRA F. A., An error analysis for the Secant method, Numer. Math. 38, 1982, 427-445. (1982) Zbl0465.65033MR0654108
  8. POTRA F. A., Sharp error bounds for a class of Newton-like methods, Libertas Mathematica 5, 1985, 71-84. (1985) Zbl0581.47050MR0816258
  9. POTRA F. A., PTÁK V., Nondiscrete induction and iterative processes, Pitman Publ. Boston, 1984. (1984) Zbl0549.41001MR0754338
  10. PTÁK V., Nondiscrete mathematical induction and iterative existence proofs, Linear Algebra Appl. 13, 1976, 223-236. (1976) MR0394119
  11. SCHMIDT J. W., Regula-Falsi Verfahren mit konsistenter Steigung und Majoranten Prinzip, Period. Math. Hungar. 5, 3, 1974, 187-193. (1974) MR0356487
  12. SERGEEV A. S., On the method of chords Sibirsk, Mat. Z. 2, 1961, 282-289. (1961) MR0130517

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