Sums of exponentials with polynomial coefficients

摘要

A homotopy continuation method is proposed for solving an inverse interpolation problem where the data is assumed to be sampled from a system whose dynamics are given by sums of decaying exponentials with polynomial coefficients. For the coordinate function F of the homotopy method the region R of invertibility of JF, the Jacobian of F, is identified. It is noted that the geometry of the region R depends only on the exponential factors and the leading coefficients of their polynomial coefficients.