The modified moment problem in the presence of noise

The modified moment problem is little studied in the literature with respect to the classical moment problem due to the lack of experiments measuring modified moments. The modified moment problem is analyzed in this paper, when noise affects the modified moments themselves. A numerical method for solving the problem, based on regularization, is given, together with a full theoretical analysis, convergence results and an optimized algorithm. The modified moment problem is shown to be strongly superior to the classical moment problem in terms of the amplification of the error, conditioning of the matrices involved and ease of computation.