Skip to main content
SpringerLink
Log in

A generalization of regula falsi

  • Published:
Numerische Mathematik Aims and scope Submit manuscript

Summary

The method of nondiscrete mathematical induction is applied to a multistep variant of the secant method. Optimal conditions for convergence as well as error estimates, sharp in every step, are obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Helfrich, H.P.: Ein modifiziertes Newtonsches Verfahren. Funktionalanalytische Methoden d. numer. Math., ISNM 12, S. 61–70. Basel: Birkhäuser 1969

    Google Scholar 

  2. Hofmann, W.: Konvergenzsätze für Regula-Falsi-Verfahren. Arch. Rational Mech. Anal.44, 296–309 (1972)

    Google Scholar 

  3. Laasonen, P.: Ein überquadratisch konvergenter iterativer Algorithmus. Ann. Acad. Sci. Fenn., Ser. A, Mathematica450, 1–10 (1969)

    Google Scholar 

  4. Potra, F.-A.: On a modified secant method. L'Analyse numérique et la théorie de l'approximation8, 203–214 (1979)

    Google Scholar 

  5. Potra, F.-A.: An application of the induction method of V. Pták to the study of Regula Falsi. Preprint Increst11 (1979)

  6. Potra, F.-A., Pták, V.: Nondiscrete induction and Laasonen's method. Preprint Increst12 (1979)

  7. Pták, V.: Deux théorèmes de factorisation. C. R. Acad. Sci. Paris278, 1091–1094 (1974)

    Google Scholar 

  8. Pták, V.: A theorem of the closed graph type. Manuscripta Math.13, 109–130 (1974)

    Google Scholar 

  9. Pták, V.: Nondiscrete mathematical induction and iterative existence proofs. Linear Algebra and Appl.13, 223–236 (1979)

    Google Scholar 

  10. Pták, V.: Nondiscrete mathematical induction. In: General topology and its relations to modern analysis and algebra IV. Lecture Notes in Mathematics Vol. 609 Berlin-Heidelberg-New York: Springer 1977

    Google Scholar 

  11. Sergeev, A.S.: O metode chord. Sibirsk. Mat. Z.2, 282–289 (1961)

    Google Scholar 

  12. Schmidt, J.W.: Eine Übertragung der Regula Falsi auf Gleichungen in Banachraum I, II. Z. Angew. Math. Mech.43, 1–8, 97–110 (1963)

    Google Scholar 

  13. Schmidt, J.W., Schwetlick, H.: Ableitungsfreie Verfahren mit höherer Konvergenzgeschwindigkeit. Computing3, 215–226 (1968)

    Google Scholar 

  14. Schröder, J.: Nichtlineare Majoranten beim Verfahren der schrittweisen Näherung. Arch. Math. (Basel)7, 471–484 (1956)

    Google Scholar 

  15. Ulm, S.: Printzip majorant i metod chord. IAN ESSR, Ser Fiz-matem I Tehn.3, 217–227 (1964)

    Google Scholar 

  16. Ulm, S.: Ob obobscennych razdelennych raznostjach, I, II. IAN ESSR, Ser Fiz-Matem I Tehn.16, 13–26, 146–156 (1967)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, National Institute for Scientific and Technical Creation, Bd. Păcii 220, 77538, Bucharest, România

    Florian A. Potra

  2. Institute of Mathematics, Czechoslovak Academy of Sciences, Zitna 25, 11567, Praha 1, Czechoslovakia

    Vlastimil Pták

Authors
  1. Florian A. Potra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vlastimil Pták
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Potra, F.A., Pták, V. A generalization of regula falsi. Numer. Math. 36, 333–346 (1980). https://doi.org/10.1007/BF01396659

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01396659

Subject Classifications

Search

Navigation