Finite moment problems: geometry of the data space and conditioned maximum entropy solutions

The existence of maximum entropy solutions for a wide class of reduced moment problems on arbitrary open subsets of ℝd is considered. In particular, new results for the case of unbounded domains are obtained. A precise condition is presented under which solvability of the moment problem implies existence of a maximum entropy solution.

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Electronic neural net algorithm for maximum entropy solutions to ill-posed problems. II. Multiply connected electronic circuit implementation

IEEE Transactions on Circuits and Systems ◽

10.1109/31.45695 ◽

1990 ◽

Vol 37 (1) ◽

pp. 110-113 ◽

Cited By ~ 1

Author(s):

C.R.K. Marrian ◽

I.A. Mack ◽

C. Banks ◽

M.C. Peckerar

Keyword(s):

Maximum Entropy ◽

Electronic Circuit ◽

Entropy Solutions ◽

Neural Net ◽

Circuit Implementation ◽

Multiply Connected ◽

Ill Posed ◽

Electronic Circuit Implementation

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Chebyshev Moment Problems: Maximum Entropy and Kernel Polynomial Methods

Maximum Entropy and Bayesian Methods ◽

10.1007/978-94-011-5430-7_22 ◽

1996 ◽

pp. 187-194 ◽

Cited By ~ 2

Author(s):

R. N. Silver ◽

H. Roeder ◽

A. F. Voter ◽

J. D. Kress

Keyword(s):

Maximum Entropy ◽

Moment Problems ◽

Polynomial Methods

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Maximum Entropy and Moment Problems

Real Analysis Exchange ◽

10.14321/realanalexch.29.2.0607 ◽

2004 ◽

Vol 29 (2) ◽

pp. 607 ◽

Cited By ~ 1

Author(s):

C.-G. Ambrozie

Keyword(s):

Maximum Entropy ◽

Moment Problems

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On Polynomial Maximum Entropy Method for Classical Moment Problem

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.2014.m504 ◽

2015 ◽

Vol 8 (1) ◽

pp. 117-127

Author(s):

Jiu Ding ◽

Noah H. Rhee ◽

Chenhua Zhang

Keyword(s):

Maximum Entropy ◽

Moment Problem ◽

Maximum Entropy Method ◽

Entropy Method ◽

Moment Problems ◽

Monomial Basis ◽

Ill Conditioning ◽

Legendre Moment ◽

Hausdorff Moment Problem ◽

Classical Moment Problem

AbstractThe maximum entropy method for the Hausdorff moment problem suffers from ill conditioning as it uses monomial basis {1,x,x2,...,xn}. The maximum entropy method for the Chebyshev moment probelm was studied to overcome this drawback in. In this paper we review and modify the maximum entropy method for the Hausdorff and Chebyshev moment problems studied in and present the maximum entropy method for the Legendre moment problem. We also give the algorithms of converting the Hausdorff moments into the Chebyshev and Lengendre moments, respectively, and utilizing the corresponding maximum entropy method.

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