An extension of the multivariate component-resolution method to three components

Abstract The extension of the multivariate curve resolution theory presented is based on the minimum assumptions of non-negativity of sensor responses and non-negativity of quantities of components, as given by Lawton and Sylvestre. The theory is explicitly given for three components, while the algorithms developed may potentially be extended to the more general n -component case. The analytical solution to the problem of defining the physically permitted regions for the sensor responses (“spectra”) or quantity profiles of pure components is given. Implementations of the algorithms developed are used for finding the permitted ranges of the pure component spectra from mixture spectra. Extensions of the minimal assumption theory are suggested.