A New Algorithm to Fit Exponential Decays
For practitioners fitting exponential decays, this provides a theoretically grounded algorithm that avoids the need for initial guesses, but the restriction to a specific form limits its impact.
The paper proves quasiconvexity of the error function for fitting exponential decays of the form f(t)=λ₁exp(kt)+λ₂, and proposes an algorithm that does not require an initial guess. No concrete numerical results are reported.
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 $f (t) = λ_1 \exp(kt) + λ_2.$ 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.