This paper focuses on why the regular least-squares fitting technique is unstable when used to fit exponential functions to signal waveforms, since such functions are highly correlated. It talks about alternative approaches, such as the search method, which has a slow convergence rate of 1/N1/M, for M parameters, where N is the number of computations performed. We have used the Monte Carlo method, utilizing both search and random walk, to devise a stable least-squares fitting algorithm that converges rapidly at a rate 1/N1/2, regardless of the number of parameters used in fitting the waveforms. The Monte Carlo approach has been tested for computed data-with and without noise, and by fitting actual experimental signal waveforms associated with optogalvanic transitions recorded with a hollow cathode discharge tube containing a mixture of neon (Ne) and carbon monoxide (CO) gases, and has yielded excellent results, making the developed algorithm both stable and fast for today's personal computers.
