Stabilized Solution and Numerical Simulation for a Two-Dimensional Hausdorff Moment Problem

In this paper we consider a two-dimensional Hausdorff moment problem (2-D HMP) to recover an unknown function from a finite number of moments contaminated by noise. It is well known that the 2-D HMP is a severely ill-posed problem. In order to obtain a conditional stability, we transform equivalently the 2-D HMP into two 1-D HMPs. From our derived result on the 1-D HMP by using the integral equation methods, We establish a conditional stability estimate for the 2-D HMP. Based on the conditional stability, we present an algorithm with an error estimate to the reconstruction of the function. Finally we provide some numerical examples to test the theoretical results. The numerical simulation shows the efficiency and sound implementation of the given algorithm.