A ray casting method for the computation of the area of feasible solutions for multicomponent systems: Theory, applications and FACPACK-implementation

- The Area of feasible solutions (AFS) represents the ambiguity of MCR factorizations.
- Ray casting is a universal tool for computing the AFS for multicomponent systems.
- The simplicity of ray casting is based on the gap-free intersection property of any AFS.
- An implementation of the ray casting algorithm is available in the FACPACK software

Multivariate curve resolution methods suffer from the non-uniqueness of the solutions. The set of possible nonnegative solutions can be represented by the so-called Area of Feasible Solutions (AFS). The AFS for an s-component system is a bounded (s−1)-dimensional set. The numerical computation and the geometric construction of the AFS is well understood for two- and three-component systems but gets much more complicated for systems with four or even more components.This work introduces a new and robust ray casting method for the computation of the AFS for general s-component systems. The algorithm shoots rays from the origin and records the intersections of these rays with the AFS. The ray casting method is computationally fast, stable with respect to noise and is able to detect the various possible shapes of the AFS sets. The easily implementable algorithm is tested for various three- and four-component data sets.

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