Newton iteration, conditioning and zero counting
Numerical Analysis
2012-11-12 v1
Abstract
Those lectures revolve around the following problem: given a system of n real polynomials in n variables, count the number of real roots. The first lecture is a course on Newton iteration and alpha-theory. The second describes an inclusion-exclusion algorithm for real polynomials, developed by Felipe Cucker, Teresa Krick, Mario Wschebor and myself. The third lecture introduces tools for complexity analysis of numerical algorithms, and uses those tools to analyze our root-counting algorithm.
Cite
@article{arxiv.1211.2120,
title = {Newton iteration, conditioning and zero counting},
author = {Gregorio Malajovich},
journal= {arXiv preprint arXiv:1211.2120},
year = {2012}
}
Comments
Lecture notes for the Santal\'o summer school on Recent Advances in Real Complexity and Computation, Universidad Internacional Men\'endez Pelayo, Santander, july 2012