Nonlinear Equations in One Variable

Ulrich Kulisch, Rolf Hammer, Matthias Hocks and Dietmar Ratz
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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

Chapter Chapter 6 in C++ Toolbox for Verified Computing I, 1995, pp 93-112 from Springer

Abstract: 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; Actual Interval; Interval Vector; Empty Interval (search for similar items in EconPapers)
Date: 1995
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DOI: 10.1007/978-3-642-79651-7_6

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