Parameter estimation of monomial-exponential sums in one and two variables

We propose a matrix-pencil method to identify monomial-exponential sums.In the univariate case, it is based on the QR factorization of Hankel matrices.In the bivariate case, it assures the same accuracy of the univariate case. In this paper we propose a matrix-pencil method for the numerical identification of the parameters of monomial-exponential sums in one and two variables. While in the univariate case the proposed method is a variant of that developed by the authors in a preceding paper, the bivariate case is treated for the first time here. In the bivariate case, the method we propose, easily extendible to more variables, reduces the problem to a pair of univariate problems and subsequently to the solution of a linear system. As a result, the relative errors in the univariate and in the bivariate case are almost of the same order.