Hausdorff moment problem and Maximum Entropy: On the existence conditions

2011 ◽  
Vol 218 (2) ◽  
pp. 430-433 ◽  
Author(s):  
M. Frontini ◽  
A. Tagliani
Keyword(s):  
Maximum Entropy ◽  
Moment Problem ◽  
Existence Conditions ◽  
Hausdorff Moment Problem

On Polynomial Maximum Entropy Method for Classical Moment Problem

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.

An algorithm for the Hausdorff moment problem

1982 ◽  
Vol 39 (2) ◽  
pp. 231-238 ◽  
Author(s):  
G. Greaves
Keyword(s):  
Moment Problem ◽  
Hausdorff Moment Problem
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