Confluent Prony approximation (Q1192162)

Given \(2n\) data, the interpolating exponential sum \(\sum^ n_{i=1}A_ i\exp(\alpha_ ix)\) is to be determined. If the \(x_ j\)'s are equally spaced, then Prony's classical method may be applied. Typically, first the quantities \(\exp(\alpha_ i h)\) are obtained as the roots of a polynomial of degree \(n\). There is no analogon, if the points are not equally spaced. The author observes that on the other hand the confluent case is easily solved, i.e. the case in which the data are the derivatives at one point. Here the \(\alpha_ i\)'s are obtained from a polynomial equation. The author wonders that this case is not found in textbooks.