Comparison of interpolation polynomials with divided differences, interpolation polynomials with finite differences, and quadratic functions obtained by the least squares method in modeling of chromatographic responses

Abstract

A novel approach to mathematical modeling of chromatographic responses based on interpolation polynomials with divided differences and with finite differences is discussed. These interpolational techniques as well as traditionally applied second-order polynomial models obtained by least squares are compared. Interpolation techniques can be useful in situations where commonly used linear or quadratic models are not applicable: when the nature of dependence is complex or the investigated factor intervals are broad. The three analyzed modeling techniques are incorporated in a design of experiments methodology for systematic development and optimization of liquid chromatographic methods. The direct modeling of retention factors is carried out first, while the objective function for final quality measurement is calculated last. An interpolation polynomial with divided differences resulted in a high quality fit compared with the results obtained by the other two modeling approaches and succeeded in locating the desired optimum. It is shown that this modeling technique can be a useful alternative for modeling of chromatographic responses. © 2013 John Wiley & Sons, Ltd.