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Heuristic solutions to polynomial moment problems with some convex entropic objectives

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Abstract

We are asking to estimate a nonnegative density\(\bar x\) on ℝm, given some of its algebraic or trigonometric moments. The maximum entropy method is to introduce an entropy-like objective function and then solve a convex minimization programming with some linear constraints. In the existing literature, Newton's method or some other iteration methods are used to solve its dual problem. In this paper, special structures of the problem have been discovered when we use some particular entropies, which include Boltzmann-Shannon entropy and Burg's entropy. Useful linear relationships among the moments help us to set up very fast and effective algorithms. Numerical computations and comparison are also presented.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, School of Mathematical Sciences, Lakehead University, P7B 5E1, Thunder Bay, Ontario, Canada

    Wanzhen Huang

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  1. Wanzhen Huang
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Communicated by C. Brezinski

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Huang, W. Heuristic solutions to polynomial moment problems with some convex entropic objectives. Numer Algor 12, 297–308 (1996). https://doi.org/10.1007/BF02142809

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  • DOI: https://doi.org/10.1007/BF02142809

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