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Nonlinear Equations in One Variable

In: C++ Toolbox for Verified Computing I

Author

Listed:
  • Ulrich Kulisch

    (Universität Karlsruhe, Institut für Angewandte Mathematik)

  • Rolf Hammer

    (Universität Karlsruhe, Institut für Angewandte Mathematik)

  • Matthias Hocks

    (Universität Karlsruhe, Institut für Angewandte Mathematik)

  • Dietmar Ratz

    (Universität Karlsruhe, Institut für Angewandte Mathematik)

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.

Suggested Citation

  • Ulrich Kulisch & Rolf Hammer & Matthias Hocks & Dietmar Ratz, 1995. "Nonlinear Equations in One Variable," Springer Books, in: C++ Toolbox for Verified Computing I, chapter 0, pages 93-112, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-79651-7_6
    DOI: 10.1007/978-3-642-79651-7_6
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