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Evaluation of Polynomials

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

Abstract

In this chapter, we consider the evaluation of a polynomial function of a single variable. We usually compute the value of an arithmetic function by replacing each arithmetic operation by its corresponding floating-point machine operation (see Section 3.5). Roundoff errors and cancellations sometimes cause the calculated result to be drastically wrong. For similar reasons, a naive interval evaluation of a polynomial may lead to intervals so large as to be practically useless. Roundoff and cancellation errors are especially dangerous if we are evaluating a function close to a root, as we will see in Chapter 9 when we compute verified enclosures of zeros of polynomials.

Keywords

Interval Arithmetic Error Message Maximum Accuracy Real Polynomial 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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