Algorithms for Polynomial Real Root Isolation

Abstract

This paper summarizes results obtained in the author’s Ph.D. thesis (Johnson 1991). Improved maximum computing time bounds are obtained for isolating the real roots of an integral polynomial. In addition to the theoretical results a systematic study was initiated comparing algorithms based on Sturm sequences, the derivative sequence, and Descartes’ rule of signs. The algorithm with the best theoretical computing time bound is the coefficient sign variation method, an algorithm based on Descartes’ rule of signs. Moreover, the coefficient sign variation method typically outperforms the other algorithms in practice; however, we exhibit classes of input polynomials for which each algorithm is superior.