Improving non-linear fits

TL;DR

This paper introduces a Python algorithm for non-linear fitting that combines variable projection, Newton optimization, and Bayesian priors, demonstrating effectiveness with simulated data, especially for sums of exponentials in physics applications.

Contribution

The paper presents a novel Python implementation of a non-linear fitting algorithm that integrates variable projection, Newton optimization, and Bayesian priors.

Findings

Effective fitting of sums of exponentials demonstrated

Algorithm performs well with simulated data

Suitable for applications like Lattice QCD

Abstract

In this notes we describe an algorithm for non-linear fitting which incorporates some of the features of linear least squares into a general minimum $\chi^2$ fit and provide a pure Python implementation of the algorithm. It consists of the variable projection method (varpro), combined with a Newton optimizer and stabilized using the steepest descent with an adaptative step. The algorithm includes a term to account for Bayesian priors. We performed tests of the algorithm using simulated data. This method is suitable, for example, for fitting with sums of exponentials as often needed in Lattice Quantum Chromodynamics.