An Adaptive Grid Algorithm for Computing the Homology Group of Semialgebraic Set
Data Structures and Algorithms
2019-03-07 v1 Computational Geometry
Geometric Topology
Optimization and Control
Abstract
Looking for an efficient algorithm for the computation of the homology groups of an algebraic set or even a semi-algebraic set is an important problem in the effective real algebraic geometry. Recently, Peter Burgisser, Felipe Cucker and Pierre Lairez wrote a paper [1], which made a step forward by giving an algorithm of weak exponential time. However, the algorithm is not not practical. In my thesis, I will introduce my improvement of this algorithm using an adaptive grid algorithm on the unit sphere.
Cite
@article{arxiv.1903.02388,
title = {An Adaptive Grid Algorithm for Computing the Homology Group of Semialgebraic Set},
author = {Han Jiadong},
journal= {arXiv preprint arXiv:1903.02388},
year = {2019}
}
Comments
arXiv admin note: text overlap with arXiv:1706.07473 by other authors