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We consider applications of the best L1 piecewise monotonic approximation method for the peak estimation of three sets of up to 2500 measurements of Raman, Infrared and Nuclear Magnetic Resonance (NMR)spectra. Peak estimation is an inherent problem of spectroscopy. The location of peaks and their intensities arethe signature of a sample of an organic or an inorganic compound. The diversity and the complexity of our measurements makes it a difficult test of the effectiveness of the method. We find that the method identifies efficientlypeaks and we compare to the results obtained by the analogous least squares calculations. These results havemany similarities and occasionally considerable differences due to both properties of the norms employed in theoptimization calculations and nature of the spectra. Our results may be helpful to subject analysts as part of theinformation on which decisions will be made for estimating peaks in sequences of spectra and to the developmentof new algorithms that are particularly suitable for peak estimation calculations.

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