Skip to main content

On the simultaneous determination of polynomial roots

Applications And Special Topics

Part of the Lecture Notes in Mathematics book series (LNM,volume 953)

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

5. References

  1. O. ABERTH: Iteration methods for finding all zeros of a polynomial simultaneously. Math.Comp. 27, 339–344 (1973)

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. G.ALEFELD, J.HERZBERGER: Einführung in die Intervallrechnung B.I.Wissenschaftsverlag, Mannheim, 1974

    Google Scholar 

  3. G. ALEFELD, J. HERZBERGER: On the convergence speed of some algorithms for the simultaneous approximation of polynomial roots, SIAM J.Numer.Anal. 11, 237–243 (1974)

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. W. BÖRSCH-SUPAN: A posteriori error bounds for the zeros of polynomials, Numer.Math. 5, 380–398 (1963)

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. W. BÖRSCH-SUPAN: Residuenabschätzung für Polynom-Nullstellen mittels Lagrange-Interpolation, Numer.Math. 14, 287–296 (1970)

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. D. BRAESS, K.P. HADELER: Simultaneous inclusion of the zeros of a polynomial, Numer.Math. 21, 161–165 (1973)

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. D. BRAESS, H. SPÄTH: Maßnahmen zur globalen Konvergenzerzwingung beim Newton'schen Verfahren für spezielle nichtlineare Gleichungssysteme, ZAMM 47, 409–410 (1967)

    CrossRef  MATH  Google Scholar 

  8. P. BYRNEV, K. DOCHEV: Certain modifications of Newton's method for the approximate solution of algebraic equations, Zh.Vych.Mat. 4, 915–920 (1964)

    MATH  Google Scholar 

  9. K. DOCHEV, L. ILLIEF: Über Newton'sche Iterationen, Wiss.Z.TH Dresden 12, 117–118 (1963)

    Google Scholar 

  10. E. DURAND: Solution numérique des équations algébraique (tome 1), Masson, Paris, 1960

    Google Scholar 

  11. L.W. EHRLICH: A modified Newton method for polynomials, Comm.ACM 10, 107–108 (1967)

    CrossRef  MATH  Google Scholar 

  12. L. ELSNER: A remark on simultaneous inclusions of the zeros of a polynomial by Gershgorin's theorem, Numer.Math. 21, 425–427 (1973)

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. I. GARGANTINI, P. HENRICI: Circular arithmetic and the determination of polynomial zeros, Numer.Math. 18, 305–320 (1972)

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. M. GUTKNECHT: A posteriori error bounds for the zeros of a polynomial, Numer.Math. 20, 139–148 (1972)

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. P. HENRICI: Applied and computational complex analysis, John Wiley, New York, 1974

    MATH  Google Scholar 

  16. A.S. HOUSEHOLDER: The numerical treatment of a single nonlinear equation, McGraw-Hill, New York, 1970

    MATH  Google Scholar 

  17. A.S. HOUSEHOLDER: The theory of matrices in numerical analysis, Blaisdell, New York, 1964

    MATH  Google Scholar 

  18. I.O. KERNER: Ein Gesamtschrittverfahren zur Berechnung von Nullstellen von Polynomen, Numer.Math. 8, 290–294 (1966)

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. I.O.KERNER: Simultaneous displacement of polynomial roots if real and simple, Comm.ACM, 273, (1966)

    Google Scholar 

  20. M.MARDEN: Geometry of polynomials, AMS Math.Surveys 3, 1966

    Google Scholar 

  21. L.M. MILNE-THOMPSON: The calculus of finite differences, Macmillan, London, 1933

    Google Scholar 

  22. J.W. SCHMIDT: Eine Anwendung des Brouwer'schen Fixpunktsatzes zur Gewinnung von Fehlerschranken für Näherungen von Polynomnullstellen, Beiträge zur Numerischen Mathematik 6, 158–163, (1977)

    MATH  Google Scholar 

  23. J.W. SCHMIDT, H. DRESSEL: Fehlerabschätzungen bei Polynomgleichungen mit dem Fixpunktsatz von Brouwer, Numer.Math. 10, 42–50 (1967)

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. B.T. SMITH: Error bounds for the zeros of a polynomial based upon Gershgorin's theorems, J.Assoc.Comput.Mach. 17, 661–674 (1970)

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. K.WEIERSTRASS: Neuer Beweis des Satzes, dass jede ganze rationale Funktion einer Veränderlichen dargestellt werden kann als Product aus linearen Funktionen derselben Veränderlichen, Ges.Werke 3, 251–269

    Google Scholar 

  26. W.WERNER: A generalized Frobenius normal form and some applications, submitted for publication

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Werner, W. (1982). On the simultaneous determination of polynomial roots. In: Ansorge, R., Meis, T., Törnig, W. (eds) Iterative Solution of Nonlinear Systems of Equations. Lecture Notes in Mathematics, vol 953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069383

Download citation

  • DOI: https://doi.org/10.1007/BFb0069383

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11602-8

  • Online ISBN: 978-3-540-39379-5

  • eBook Packages: Springer Book Archive