How to find all roots of complex polynomials by Newton's method

Authors
Hubbard, J Schleicher, D Sutherland, S
Citation
J. Hubbard et al., How to find all roots of complex polynomials by Newton's method, INVENT MATH, 146(1), 2001, pp. 1-33
Citations number
25
Categorie Soggetti
Mathematics
Journal title
INVENTIONES MATHEMATICAE
ISSN journal
00209910 → ACNP
Volume
146
Issue
1
Year of publication
2001
Pages
1 - 33
Database
ISI
SICI code
0020-9910(200110)146:1<1:HTFARO>2.0.ZU;2-4
Abstract
We investigate Newton's method to find roots of polynomials of fixed degree d, appropriately normalized: we construct a finite set of points such that , for every root of every such polynomial, at least one of these points wil l converge to this root under Newton's map. The cardinality of such a set c an be as small as 1.11 d log(2) d; if all the roots of the polynomial are r eal, it can be 1.30 d.