Approximation by Exponential Sums

The rational functions and exponential sums belong to those concrete families of functions which are the most frequently studied in nonlinear approximation theory. The starting point in the consideration of exponential sums is an approximation problem often encountered for the analysis of decay processes in natural sciences. A given empirical function on a real interval is to be approximated by sums of the form $$ \sum\limits_{v = 1}^n {{\alpha _v}{e^{{t_v}x}}} $$ where the parameters α _v and t _v are to be determined, while n is fixed.