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Resolving Factor Analysis, RFA

Resolving Factor Analysis, RFA, is an attempt to introduce the strengths of the Newton-Gauss algorithm into the model-free analysis methodology. As [Pg.290]

For a three component system, the matrix T has nine elements and thus it appears that C and eventually the sum of squares are a function of nine parameters. As we will see in a moment there are actually fewer, only six, parameters to be fitted. The idea of RFA is to use the Newton-Gauss algorithm to fit this rather small number of parameters in T. [Pg.291]

An important issue needs to be discussed next. Multiplying a column of C with any number and its corresponding row of A with the inverse of that number, does not affect the product CA and thus this factor is not determined at all. It can be freely chosen. Due to this multiplicative ambiguity, only the shapes of the concentration profiles (and component spectra) can be determined by any model-free method and only additional quantitative information allows the absolute determination of C and A. [Pg.291]

Multiplying a concentration profile, or column of C, with a factor is equivalent to multiplication of the corresponding column of T with the same factor. Any one element of each column vector of T can be chosen freely while the other elements in that column define the shape of the concentration profile. In order to avoid numerical problems with very small or very large numbers in each column of T, we choose the largest absolute element of each column of the matrix of initial guesses TgUess and keep it [Pg.291]

The Newton-Gauss algorithm (ng Jm3. m), is called from Main RFA.m, and requires a Matlab function that computes the residuals as a function of the parameters T, as defined in equation (5.54). This calculation is performed in the Matlab function Rcalc RFA. m. [Pg.292]


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