# Self Modeling Curve Resolution

**William H. Lawton****Edward A. Sylvestre**

CiteWeb id: 20120000746

CiteWeb score: 714

This paper presents a method for determining the shapes of two overlapping functionsfi(x) andf2(x) from an observed set of additive mixtures, {aifi(x) + lif2(x); i = 1, ... , n}, of the two functions. This type of problem arises in the fields of spectrophotometry, chromatography, kinetic model building, and many others. The methods described by this paper are based on the use of principal component techniques, and produce two bands of functions, each of which contains one of the unknown, underlying functions. Under certain mild restrictions on the fi(x), each band reduces to a single curve, and the fj(x) are completely determined by the analysis. 1. THE PROBLEM The techniques described in this paper may be applied to any experiment whose outcome is a continuous curve Y(X) which is an additive mixture of two unknown, nonnegative, linearly independent functions. That is, Y(X) is of the form Y(X) = afl(X) + /f2(X), L1 < X < L2 (1) where the f i(X) are unknown, nonnegative, linearly independent functions. We shall also assume that the fi(X) are normalized to unit area, so that

**Self Modeling Curve Resolution**" is placed in the Top 10000 in category Mathematics.

- www.jstor.org/stable/1267173
- natasha.eng.usf.edu/gilbert/courses/modelandanalysis/portfolios/1_project_13/chaudhari_project_13.pdf
- dx.doi.org/10.1080/00401706.1971.10488823
- www.tandfonline.com/doi/abs/10.1080/00401706.1971.10488823
- ci.nii.ac.jp/naid/30022451834
- amstat.tandfonline.com/doi/abs/10.1080/00401706.1971.10488823
- www.jstor.org/pss/1267173

William H. Lawton, Edward A. Sylvestre,

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