On Polynomial Maximum Entropy Method for Classical Moment Problem

Abstract

The maximum entropy method for the Hausdorff moment problem suffers from ill conditioning as it uses monomial basis {1,$x$,$x^2$,\u00b7\u00b7\u00b7,$x^n$}. 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.