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.

mxpfit 是一款采用 C++ 编写的库，旨在通过带复参数的多指数和求解函数的最优近似。该库提供了一套接口，可基于均匀网格上的采样数据，借助由 Potts 与 Tasche 提出的旋转不变性快速信号参数估计（fast Estimation of Signal Parameters via Rotational Invariance Techniques，ESPRIT）算法来估算指数项与系数，该算法最初发表于《应用数值数学》（Appl. Numer. Math. 88 (2015) 31）。即便采样数据包含噪声，该库仍可高效地从中估算出所需参数。此外，库中还集成了一种改进的平衡截断算法，用于求解阶数更小的多指数和。上述特性可用于获取解析函数或大规模数值采样数据集的最优多指数和近似。