A New Algorithm to Fit Exponential Decays

TL;DR

This paper introduces a novel algorithm for fitting exponential decay models that leverages the quasiconvexity of the error function, enabling efficient estimation without initial guesses.

Contribution

The paper proves quasiconvexity of the error function for exponential decay fitting and proposes a new algorithm that does not require initial guesses.

Findings

Algorithm effectively fits exponential decays.

No initial guess needed for the estimation.

The approach is based on quasiconvexity proof.

Abstract

This paper deals with some nonlinear problems which exponential and biexponential decays are involved in. A proof of the quasiconvexity of the error function in some of these problems of optimization is presented. This proof is restricted to fitting observations by means of exponentials having the form $f (t) = {\lambda}_1 \exp(kt) + {\lambda}_2.$ Based on its quasiconvexity, we propose an algorithm to estimate the best approximation to each of these decays. Besides, this algorithm does not require an initial guess.