Newton's method with deflation for isolated singularities of polynomial systems
Numerical Analysis
2007-05-23 v2 Algebraic Geometry
Abstract
We present a modification of Newton's method to restore quadratic convergence for isolated singular solutions of polynomial systems. Our method is symbolic-numeric: we produce a new polynomial system which has the original multiple solution as a regular root. Using standard bases, a tool for the symbolic computation of multiplicities, we show that the number of deflation stages is bounded by the multiplicity of the isolated root. Our implementation performs well on a large class of applications.
Cite
@article{arxiv.math/0408419,
title = {Newton's method with deflation for isolated singularities of polynomial systems},
author = {Anton Leykin and Jan Verschelde and Ailing Zhao},
journal= {arXiv preprint arXiv:math/0408419},
year = {2007}
}
Comments
15 pages; preliminary version presented as poster at ISSAC 2004, 6 July 2004, conjecture on number of deflations is proven