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Algebraic-exponential Data Recovery from Moments

Lookup NU author(s): Professor Mihai Putinar


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Let be a bounded open subset of Euclidean space whose boundary is algebraic, i.e., contained in the real zero set of finitely many polynomials. Under the assumption that the degree d of this variety is given, and the power moments of the Lebesgue measure on are known up to order 3d, we describe an algorithmic procedure for obtaining a polynomial vanishing on . The particular case of semi-algebraic sets defined by a single polynomial inequality raises an intriguing question related to the finite determinateness of the full moment sequence. The more general case of a measure with density equal to the exponential of a polynomial is treated in parallel. Our approach relies on Stokes' Theorem on spaces with singularities and simple Hankel-type matrix identities.

Publication metadata

Author(s): Lasserre JB, Putinar M

Publication type: Article

Publication status: Published

Journal: Discrete & Computational Geometry

Year: 2015

Volume: 54

Issue: 4

Pages: 993-1012

Print publication date: 01/12/2015

Online publication date: 26/10/2015

Acceptance date: 29/09/2015

ISSN (print): 0179-5376

ISSN (electronic): 1432-0444

Publisher: Springer


DOI: 10.1007/s00454-015-9739-1


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