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A New Method for Polynomial Real Root Isolation

Summary: A New Method for Polynomial
Real Root Isolation
Alkiviadis G. Akritas (North
Carolina State University)
Abstract. A new method is presented for the iso-
lation of the real roots of a given integral,
univariate, square-free polynomial P. This method
is based on Vincent's theorem and only uses:
(i) Descartes' rule of signs, and (ii) transforma-
l , x' = a2 + ~,,tlons of the form x = aI + ~,
x" = a3 + ~........ for positive, integral ai's.
The key element in this procedure is the calcula-
tion of the quantities al,a2,a 3..... We compute
them as "positive lower root bounds" of polynomials
and the resulting algorithm has the best theoreti-
cal computing time achieved thus far. Empirical
results also verify the superiority of our method
over all others existing.
I. Introduction


Source: Akritas, Alkiviadis G. - Department of Computer and Communication Engineering, University of Thessaly


Collections: Computer Technologies and Information Sciences