Newton-Algorithmen zur Bestimmung von Polynomwurzeln unter Verwendung komplexer Kreisarithmetik

  • G. Glatz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 29)


Suppose that some zeros of a (complex) polynomial are known to lie in specified circular regions. Then there are given algorithms to determine the remaining zeros with simultaneous computation of error bounds. The algorithms are based upon a modified Newton's method, their theoretical foundation and their application make use of circular arithmetic, an extension of interval arithmetic to the complex plane. The algorithms were constructed with special regard to multiple zeros and clusters of zeros. With suitable starting-approximations an approximation can be found iteratively together with an error bound for each zero.


Interval Arithmetic Multiple Zero Simultaneous Computation Circular Arithmetic 
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  1. [1]
    GARGANTINI, I. and HENRICI, P.: Circular Arithmetic and the Determination of Polynomial Zeros, Numer.Math. 18, 305–320 (1972).CrossRefGoogle Scholar
  2. [2]
    KRIER, N.: Komplexe Kreisarithmetik, Dissertation am Institut für Praktische Mathematik, Universität Karlsruhe (1973).Google Scholar
  3. [3]
    NICKEL, K.: Die numerische Berechnung der Wurzeln eines Polynoms, Numer.Math. 9, 80–98 (1966).Google Scholar
  4. [4]
    NICKEL, K.: Fehlerschranken zu Näherungswerten von Polynomwurzeln, Computing 6, 9–27 (1970).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • G. Glatz
    • 1
  1. 1.Institut für Praktische MathematikUniversität KarlsruheBRD

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