On Polynomial Maximum Entropy Method for Classical Moment Problem
Document Type
Article
Publication Date
2-2016
Department
Mathematics
Abstract
The maximum entropy method for the Hausdorff moment problem suffers from ill conditioning as it uses monomial basis {1,chi,chi(2),...,chi(n)}. The maximum entropy method for the Chebyshev moment probelm was studied to overcome this drawback in [4]. In this paper we review and modify the maximum entropy method for the Hausdorff and Chebyshev moment problems studied in [4] 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.
Publication Title
Advances in Applied Mathematics and Mechanics
Volume
8
Issue
1
First Page
117
Last Page
127
Recommended Citation
Ding, J.,
Rhee, N. H.,
Zhang, C.
(2016). On Polynomial Maximum Entropy Method for Classical Moment Problem. Advances in Applied Mathematics and Mechanics, 8(1), 117-127.
Available at: https://aquila.usm.edu/fac_pubs/17554