Generalization of rank reduction problems with Wedderburn's formula

Abstract

In first-and second-order calibration methods based on spectroscopic data, the calculation of the space spanned by the spectra of the interferences has been an important research subject for, among many other applications, calculating the net analyte signal and obtaining figures of merit. Recently, many different calculation methods have been introduced. We show that the calculation of this space can be interpreted from a unified point of view, namely from the rank-one downdating Wedderburn formula. This formula enables one to better understand the properties of the calculation methods currently available. A number of recently introduced signal-preprocessing methods also fit into the proposed framework.

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