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Numerische Mathematik

, Volume 69, Issue 3, pp 353–372 | Cite as

Weierstrass formula and zero-finding methods

  • Miodrag S. Petkovi\'c
  • Carsten Carstensen
  • Miroslav Trajkov\'\i c

Summary.

Classical Weierstrass' formula [29] has been often the subject of investigation of many authors. In this paper we give some further applications of this formula for finding the zeros of polynomials and analytic functions. We are concerned with the problems of localization of polynomial zeros and the construction of iterative methods for the simultaneous approximation and inclusion of these zeros. Conditions for the safe convergence of Weierstrass' method, depending only on initial approximations, are given. In particular, we study polynomials with interval coefficients. Using an interval version of Weierstrass' method enclosures in the form of disks for the complex-valued set containing all zeros of a polynomial with varying coefficients are obtained. We also present Weierstrass-like algorithm for approximating, simultaneously, all zeros of a class of analytic functions in a given closed region. To demonstrate the proposed algorithms, three numerical examples are included.

Mathematics Subject Classification (1991):65H05 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Miodrag S. Petkovi\'c
    • 1
  • Carsten Carstensen
    • 2
  • Miroslav Trajkov\'\i c
    • 1
  1. 1.Faculty of Electronic Engineering, University of Ni\v s, 18000 Ni\v s, Yugoslavia YU
  2. 2.Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4A5, UK GB

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