Communications in Mathematical Sciences

Volume 8 (2010)

Number 2

Special Issue on the Occasion of Andrew Majda’s Sixtieth Birthday: Part II

The multidimensional maximum entropy moment problem: a review of numerical methods

Pages: 377 – 392

DOI: http://dx.doi.org/10.4310/CMS.2010.v8.n2.a5

Author

Rafail V. Abramov

Abstract

Recently the author developed a numerical method for the multidimensional momentconstrained maximum entropy problem, which is practically capable of solving maximum entropy problems in the two-dimensional domain with moment constraints of order up to 8, in the threedimensional domain with moment constraints of order up to 6, and in the four-dimensional domain with moment constraints of order up to 4, corresponding to the total number of moment constraints of 44, 83 and 69, respectively. In this work, the author brings together key algorithms and observations from his previous works as well as other literature in an attempt to present a comprehensive exposition of the current methods and results for the multidimensional maximum entropy moment problem.

Keywords

Maximum entropy problem; moment constraints; numerical methods

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