A New Method for Real Root Isolation of Univariate Polynomials

A new algorithm for real root isolation of univariate polynomials is proposed, which is mainly based on exact interval arithmetic and bisection method. Although exact interval arithmetic is usually supposed to be inefficient, our algorithm is surprisingly fast because the termination condition of our algorithm is different from those of existing algorithms which are mostly based on Descartes’ rule of signs or Vincent’s theorem and we decrease the times of Taylor shifts in some cases. We test our algorithm on a large number of examples from the literature and report the performance. Mathematics Subject Classification (2000). 68W30. Keywords. Real root isolation, interval arithmetic, interval Newton operator, bisection method, Maple.

• Type: Journal
• Year: 2007
• Where: MICS
• Authors: Ting Zhang, Bican Xia
• Keywords: Algorithm, Exact Interval Arithmetic, MICS 2007, Real Root Isolation