Extension of self-modeling curve resolution to mixtures of more than three components: Part 1. Finding the basic feasible region

Abstract

Henry, R.C. and Kim, B.M., 1990. Extension of self-modeling curve resolution to mixtures of more than three components. Part 1. Finding the basic feasible region. Chemometrics and Intelligent Laboratory Systems, 8: 205–216. Self-modeling curve resolution attempts to find all possible solutions to a mixture problem which obey certain natural physical constraints expressed as linear inequalities in an eigenspace. The basic feasible region is the region of the eigenspace defined by the intersection of these constraints. A method is given to determine this region for a mixture of any number of components. The outer boundary of the region is found using linear programming methods to determine all its vertices. The vertices of the inner boundary are also found by linear programming; however, the constraints are formulated in a different eigenspace. The method is demonstrated on a set of simulated airborne particulate composition data. A more complete solution to the mixture problem requires additional physical constraints on the solutions. Incorporating these in the model will be the subject of a later paper. The effects of random errors in the data will also be considered at a later time.