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Title: The inverse moment problem for convex polytopes
Authors: Gravin, Nick.
Lasserre, Jean.
Pasechnik, Dmitrii V.
Robins, Sinai.
Issue Date: 2012
Source: Gravin, N., Lasserre, J., Pasechnik, D. V., & Robins, S. (2012). The Inverse Moment Problem for Convex Polytopes. Discrete & Computational Geometry, 48(3), 596-621.
Series/Report no.: Discrete & computational geometry
Abstract: We present a general and novel approach for the reconstruction of any convex d-dimensional polytope P, assuming knowledge of finitely many of its integral moments. In particular, we show that the vertices of an N-vertex convex polytope in ℝ d can be reconstructed from the knowledge of O(DN) axial moments (w.r.t. to an unknown polynomial measure of degree D), in d+1 distinct directions in general position. Our approach is based on the collection of moment formulas due to Brion, Lawrence, Khovanskii–Pukhlikov, and Barvinok that arise in the discrete geometry of polytopes, combined with what is variously known as Prony’s method, or the Vandermonde factorization of finite rank Hankel matrices.
ISSN: 0179-5376
DOI: 10.1007/s00454-012-9426-4
Rights: © 2012 Springer Science+Business Media, LLC.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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