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Nonlinear Equations in One Variable

  • Ulrich Kulisch
  • Rolf Hammer
  • Dietmar Ratz
  • Matthias Hocks
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 21)

Abstract

One of the most important tasks in scientific computing is the problem of finding zeros (or roots) of nonlinear functions. In classical numerical analysis, root-finding methods for nonlinear functions begin with an approximation and apply an iterative method (such as Newton’s or Halley’s methods), which hopefully improves the approximation. It is a myth that no numerical algorithm is able to compute all zeros of a nonlinear equation with guaranteed error bounds, or even more, that no method is able to give concrete information about the existence and uniqueness of solutions of such a problem.

Keywords

Interval Arithmetic Extended Interval Error Code Actual Interval Interval Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Ulrich Kulisch
    • 1
  • Rolf Hammer
    • 1
  • Dietmar Ratz
    • 1
  • Matthias Hocks
    • 1
  1. 1.Institut für Angewandte MathematikUniversität KarlsruheKarlsruheGermany

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