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We present a method for reducing the problem of solving a certain inhomogeneous system of polynomial equations in 2N variables into the problem of solving two linear systems of size N and rooting a degree N polynomial in one variable. Algorithmically, the computational complexity of this process is at most O(N 2 log(N)). One importance of this system lies in that its solutions can be identied with the parameters of a best approximation (in a certain sense) of a data set within a nite dimensional parametrized space of functions. We explicitly present examples of tting a sum of complex exponentials to a one-dimensional data set.

A solution to certain polynomial equations with applications to nonlinear fitting