Document Type

Article

Publication Date

2006

Publication Title

Journal of Information & Computational Science

Additional Publication URL

http://www.joics.com

Abstract

This paper focuses on why the regular least{squares ¯tting technique is unstable when used to ¯t 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 ¯tting algorithm that converges rapidly at a rate 1=N1=2, regardless of the number of parameters used in ¯tting the waveforms. The Monte Carlo approach has been tested for computed data|with and without noise, and by ¯tting 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.

Rights

This article was originally published in Journal of Information & Computational Science,2006, Volume 3, Issue 4.

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