The inverse moment problem for convex polytopes
Numerical Analysis
2012-09-13 v2 Computational Geometry
Algebraic Geometry
Combinatorics
Abstract
The goal of this paper is to present a general and novel approach for the reconstruction of any convex d-dimensional polytope P, from knowledge of its moments. In particular, we show that the vertices of an N-vertex polytope in R^d can be reconstructed from the knowledge of O(DN) axial moments (w.r.t. to an unknown polynomial measure od degree D) in d+1 distinct generic directions. Our approach is based on the collection of moment formulas due to Brion, Lawrence, Khovanskii-Pukhikov, and Barvinok that arise in the discrete geometry of polytopes, and what variously known as Prony's method, or Vandermonde factorization of finite rank Hankel matrices.
Keywords
Cite
@article{arxiv.1106.5723,
title = {The inverse moment problem for convex polytopes},
author = {Nick Gravin and Jean Lasserre and Dmitrii Pasechnik and Sinai Robins},
journal= {arXiv preprint arXiv:1106.5723},
year = {2012}
}
Comments
LaTeX2e, 24 pages including 1 appendix