On Polynomial Maximum Entropy Method for Classical Moment Problem (Advances in Applied Mathematics and Mechanics, 2018)
The maximum entropy method for the Hausdorff moment problem suffersfrom ill conditioning as it uses monomial basis {1,$x$,$x^2$,\u00b7\u00b7\u00b7,$x^n$}. The maximum entropymethod for the Chebyshev moment probelm was studied to overcome this drawbackin [4]. In this paper we review and modify the maximum entropy method for theHausdorff and Chebyshev moment problems studied in [4] and present the maximumentropy method for the Legendre moment problem. We also give the algorithms ofconverting the Hausdorff moments into the Chebyshev and Lengendre moments, respectively,and utilizing the corresponding maximum entropy method.