MXPFIT: A library for finding optimal multi-exponential approximations

mxpfit is a library implemented in C++ to find optimal approximations of functions by multi-exponential sums with complex-valued parameters. The library provides an interface for evaluating exponents and coefficients from sampling data on a uniform grid using the fast Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm originally proposed by Potts and Tasche (Appl. Numer. Math. 88 (2015) 31). The parameters can be estimated efficiently from a sampling data even including noise. A modified balanced truncation algorithm to find the multi-exponential sum with a smaller order is also provided. These features are useful for finding optimal exponential sum approximations of analytic functions or large-scale numerically sampled data set.