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Title:

Polynomial-time amoeba neighborhood membership and faster localized solving

Document type:
Buchbeitrag
Author(s):
Anthony, E., S. Grant, P. Gritzmann and J.M. Rojas
Abstract:
We derive efficient algorithms for coarse approximation of complex algebraic hypersurfaces, useful for estimating the distance between an input polynomial zero set and a given query point. Our methods work best on sparse polynomials of high degree (in any number of variables) but are nevertheless completely general. The underlying ideas, which we take the time to describe without an excess of algebraic geometry terminology, come from tropical geometry. We then apply our methods to finding roots...     »
Editor:
J. Bennett, F. Vivodtzev and V. Pascucci
Book title:
Topological and Statistical Methods for Complex Data – Tackling Large-Scale, High-Dimensional, and Multivariate Data Sets
Publisher:
Springer
Year:
2015
Pages:
255-277
Reviewed:
ja
Language:
en
TUM Institution:
Lehrstuhl für Angewandte Geometrie und Diskrete Mathematik
Format:
Text
 BibTeX