Restricted Least Squares Estimation of the Spectra and Concentration of Two Unknown Constituents Available in Mixtures

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Abstract
The problem considered is the identification of two unknown chemical compounds and the estimation of their proportions in a set of unknown mixtures of the two compounds, given data that are vectors of measurements on their mixtures. It is assumed that the expected value of a mixture vector is an unknown convex linear combination of two unknown component vectors and least squares estimation is used to obtain a set of possible solutions of the mixing proportions and the component vectors. Obtaining a unique solution requires additional constraints or information. The solution set is interpreted geometrically and examples involving amino acids and light absorbance data are given.

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