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.