- Title
- Convergence of best entropy estimates
- Creator
- Borwein, J. M.; Lewis, A. S.
- Relation
- SIAM Journal on Optimization Vol. 1, Issue 2, p. 191-205
- Publisher Link
- http://dx.doi.org/10.1137/0803012
- Publisher
- Society for Industrial and Applied Mathematics (SIAM)
- Resource Type
- journal article
- Date
- 1991
- Description
- Given a finite number of moments of an unknown density ̅ x on a finite measure space, the best entropy estimate-that nonnegative density x with the given moments which minimizes the Boltzmann-Shannon entropy I(x):=∫ x log x-is considered. A direct proof is given that I has the Kadec property in L1-if Yn converges weakly to ̅y and I(yn) converges to I( ̅y ), then ynn converges to ̅y in norm. As a corollary, it is obtained that, as the number of given moments increases, the best entropy estimates converge in L1 norm to the best entropy estimate of the limiting problem, which is simply ̅ x in the determined case. Furthermore, for classical moment problems on intervals with ̅ x strictly positive and sufficiently smooth, error bounds and uniform convergence are actually obtained.
- Subject
- moment problem; entropy; Kadec; partially finite program; normal convex integrand; duality
- Identifier
- http://hdl.handle.net/1959.13/940420
- Identifier
- uon:13006
- Identifier
- ISSN:1052-6234
- Language
- eng
- Full Text
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