The Theorem of Three Circles

Fox Thomson and Wenda Li

21 August 2021

Abstract

The Descartes test based on Bernstein coefficients and Descartes’ rule of signs effectively (over-)approximates the number of real roots of a univariate polynomial over an interval. In this entry we formalise the theorem of three circles, which gives sufficient conditions for when the Descartes test returns 0 or 1. This is the first step for efficient root isolation.
BSD License

Depends On

Topics

Theories