Exact algorithms for the implementation of cauchy's rule

Abstract

Cauchy's little known rule for computing a lower (or upper) bound on the values of the positive roots of a polynomial equation has proven to be of great importance; namely it constitutes an indispensable and crucial part of the fastest method existing for the isolation of the real roots of an equation, a method which was recently developed by the author of this article. In this paper efficient, exact (infinite precision) algorithms, along with their computing time analysis, are presented for the implementation of this important rule.

Keywords:

• Analysis of (exact) algorithms
• polynomial real root isolation
• root bounds
• Cauchy's (extended) rule
• Vincent's theorem

C.R. Categories:

• 5.11
• 3.15