Quantification of the Hazards of Fitting Sums of Exponentials to Noisy Data

摘要

The ill-conditioned nature of sums-of-exponentials analyses is confirmed and quantified, using synthetic noisy data. In particular, the magnification of errors is plotted for various two-exponential models, to illustrate its dependence on the ratio of decay constants, and on the ratios of amplitudes of the contributing terms. On moving from two- to three-exponential models, the condition deteriorates badly. It is also shown that the use of 'direct' Prony-type analyses (rather than general iterative nonlinear optimisation) merely aggravates the condition. (Atomindex citation 15:007224)