Advertisement

Real arithmetic versions of simultaneous iteration methods for polynomial root finding

  • Shigeru Ando
Article
  • 13 Downloads

Abstract

Two algorithms of polynomial factorization, quadratically and cubically convergent, are presented corresponding respectively to two algorithms of polynomial root finding known as Durand-Kerner method and Aberth’s method. To apply these algorithms to the problem of factorization of a polynomial with real coefficients into at most quadratic factors within real arithmetic, a default starting value is proposed.

Key words

Durand-Kerner method Aberth’s method real-coefficient polynomial polynomial factorization 

References

  1. [1]
    O. Aberth, Iteration methods for finding all zeros of a polynomial simultaneously. Math. Comp.,23 (1973), 339–344.CrossRefMathSciNetGoogle Scholar
  2. [2]
    M. Iri, H. Yamashita, T. Terano and H. Ono, An algebraic-equation solver with global convergence property. RIMS Kokyuroku 399, 1978, 43–69.Google Scholar
  3. [3]
    M. Iri, Numerical Methods (Suuchi Keisan). Asakura Shoten, Tokyo, 1981.Google Scholar
  4. [4]
    I. O. Kerner, Ein Gesamtschrittverfahren zur Berechung der Nullstellen von Polynomen. Numer. Math.,8 (1966), 290–294.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    T. Sakurai, T. Torii and H. Sugiura, A simultaneous method for solving real-coefficient algebraic equations and its interpretation via Coulomb field. RIMS Kokyuroku 585, 1986, 1–25.Google Scholar

Copyright information

© JJAM Publishing Committee 1989

Authors and Affiliations

  • Shigeru Ando
    • 1
  1. 1.Department of MathematicsTsuda CollegeKodairaJapan

Personalised recommendations