Development on Generalized Rank Annihilation Problem by Implementing Duality

The analytical chemist is frequently confronted with the problem of analyzing complex mixtures in the presence of any component in the sample that is not included in the calibration model. In these cases, it is desirable to be able to obtain quantitative information for a particular component without concern for the rest of the components in the sample. The property of quantitation of an analyte in the presence of unknown constituents is called second-order advantage1. Additionally, in recent studies it has been shown that, when the solution is unique or information is available for obtaining the unique solution, the duality concept2, 3is a useful approach to extract information in Self Modeling Curve Resolution4, 5. In this work, a new duality based algorithm to achieve “second order advantage” and determination of standard component in the presence of unknown components is developed. For this purpose, duality relation as a powerful mathematical approach is used to define the interference(s) subspace. Afterwards, the concentration ratio of the standard component in the test sample to its amount in standard, λ, has been calculated in a systematic way. With the help of provided estimations of λ, the standard component is quantified more precisely with error intervals. Moreover, the geometrical visualizations beside algebraic formulas are used to show the quantitative analysis of this study. By illustrating the procedure in graphical plots, it has been tried to explain the details of the proposed method in an understandable way.