Calculation of lower and upper band boundaries for the feasible solutions of rank-deficient multivariate curve resolution problems

The computation of lower and upper band boundaries for the feasible solutions of multivariate curve resolution problems is an important and well-understood methodology. These techniques assume rank-regular spectral data matrices, namely the rank of the matrices equals the number of chemical species involved. For rank-deficient problems, which include linear dependencies within the pure component factors, band boundary calculations are much more complex. This paper deals with rank-deficient problems for which the rank-deficient factor is known and describes how to calculate band boundaries for the dual factor. The key tools for these band boundary computations are polytope constructions and linear programming problems to be solved for each spectral channel. Numerical studies are presented for a model problem and for two experimental data sets. •Rank-deficiency complicates the analysis of factor ambiguities in multivariate curve resolution.•An approach is presented for computing band boundaries for the factor not causing the rank-deficiency.•Linear programming from optimization makes the band boundaries accessible.