Welcome!
To use the personalized features of this site, please log in or register.
If you have forgotten your username or password, we can help.
|
 |
How to find all roots of complex polynomials by Newton’s method
| |
|
How to find all roots of complex polynomials by Newton’s method
John Hubbard1, Dierk Schleicher3 and Scott Sutherland4
| (1) |
Department of Mathematics, Malott Hall, Cornell University, Ithaca, NY 14853-4201, USA (e-mail: jhh8@cornell.edu), US |
| (2) |
Centre de Mathématiques et Informatique, Université de Provence, 39 rue F. Joliot-Curie, F-13453 Marseille cedex 13, France, FR |
| (3) |
Mathematisches Institut, Ludwig-Maximilians-Universität, Theresienstrasse 39, D-80333 München, Germany (e-mail: dierk@rz.mathematik.uni-muenchen.de), DE |
| (4) |
Institute for Mathematical Sciences, State University of New York, Stony Brook, NY 11794-3660, USA (e-mail: scott@math.sunysb.edu), US |
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 will converge to this root under Newton’s map. The cardinality of such a set can be as small as 1.11 d log 2
d; if all the roots of the polynomial are real, it can be 1.30 d.
Oblatum 24-II-2000 & 14-II-2001¶Published online: 20 July 2001
Fulltext Preview (Small, Large)
|
|
|
|
|
|