A theorem on random polynomials and some consequences in average complexity

Real polynomials have very often very few real roots, and when algorithms depend on the number of real roots of polynomials rather than on their degrees, this fact has consequences on average complexity of algorithms. In this paper we recall some classical results on the average number of real roots...

Full description

Saved in:
Bibliographic Details
Published inJournal of symbolic computation Vol. 10; no. 5; pp. 405 - 409
Main Authors Cucker, F., Roy, M.-F.
Format Journal Article
LanguageEnglish
Published Orlando, FL Elsevier Ltd 01.11.1990
London Academic Press
Subjects
Applied sciences
Exact sciences and technology
Operational research and scientific management
Operational research. Management science
Polynomial
Root
Symbolic computation
Algorithm
Computing complexity
Online AccessGet full text

Cover

More Information
Summary:Real polynomials have very often very few real roots, and when algorithms depend on the number of real roots of polynomials rather than on their degrees, this fact has consequences on average complexity of algorithms. In this paper we recall some classical results on the average number of real roots (which is in O(log n) where n is the degree of the polynomial for many natural random distributions) and use them to get estimates on the average complexity of various algorithms characterizing real algebraic numbers.
ISSN:0747-7171
1095-855X
DOI:10.1016/S0747-7171(08)80052-1