A Fast Heuristic Method for Polynomial Moment Problems with Boltzmann–Shannon Entropy | Zendy

Jonathan M. Borwein | Zendy; W. Huang | Zendy

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A Fast Heuristic Method for Polynomial Moment Problems with Boltzmann–Shannon Entropy

Author(s) -

Jonathan M. Borwein,

W. Huang

Publication year - 1995

Publication title -

siam journal on optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.066

H-Index - 136

eISSN - 1095-7189

pISSN - 1052-6234

DOI - 10.1137/0805004

Subject(s) - mathematics , moment problem , simple (philosophy) , computation , algebraic number , entropy (arrow of time) , principle of maximum entropy , heuristic , moment (physics) , mathematical optimization , combinatorics , algorithm , mathematical analysis , philosophy , statistics , physics , epistemology , quantum mechanics , classical mechanics

The authors consider the best entropy estimate to a nonnegative density x̅ on IR^m given some of its algebraic or trigonometric moments. Using the special structure of this kind of problem, a useful linear relationship among the moments is derived. A simple algorithm then provides a fairly good estimate of x̅ by just solving a couple of linear systems. Numerical computations make the algorithm seem reasonable although the theoretical convergence is still an open problem. Some notes about the error bounds are given at the end of the paper

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