Multiprecision path tracking
Numerical Analysis
2007-05-23 v1 Algebraic Geometry
Abstract
A path tracking algorithm that adaptively adjusts precision is presented. By adjusting the level of precision in accordance with the numerical conditioning of the path, the algorithm achieves high reliability with less computational cost than would be incurred by raising precision across the board. We develop simple rules for adjusting precision and show how to integrate these into an algorithm that also adaptively adjusts the step size. The behavior of the method is illustrated on several examples arising as homotopies for solving systems of polynomial equations.
Cite
@article{arxiv.math/0605105,
title = {Multiprecision path tracking},
author = {Daniel J. Bates and Andrew J. Sommese and Charles W. Wampler},
journal= {arXiv preprint arXiv:math/0605105},
year = {2007}
}