Computing the Homology of Real Projective Sets
Algebraic Geometry
2017-05-16 v2 Algebraic Topology
Numerical Analysis
Abstract
We describe and analyze a numerical algorithm for computing the homology (Betti numbers and torsion coefficients) of real projective varieties. Here numerical means that the algorithm is numerically stable (in a sense to be made precise). Its cost depends on the condition of the input as well as on its size and is singly exponential in the number of variables (the dimension of the ambient space) and polynomial in the condition and the degrees of the defining polynomials. In addition, we show that outside of an exceptional set of measure exponentially small in the size of the data, the algorithm takes exponential time.
Cite
@article{arxiv.1602.02094,
title = {Computing the Homology of Real Projective Sets},
author = {Felipe Cucker and Teresa Krick and Michael Shub},
journal= {arXiv preprint arXiv:1602.02094},
year = {2017}
}
Comments
36 pages, 2 figures