Parameter estimation of monomial-exponential sums

In this paper we propose a matrix-pencil method for the identification of parameters and coefficients of a monomial-exponential sum which can be considered as an extension of existing matrix-pencil methods for the parameter estimation of exponential sums. The technique adopted is based on properties of the finite difference equations and it overcomes the difficulty of their extension via the invertibility of the generalized Vandermonde matrix. As a result, a matrix-pencil method based on the GSVD or the SVD is proposed which allows us to identify both simple and multiple parameters. Applications of this method to various examples show its effectiveness.