Parameter Fitting via Target Testing

It is worthwhile examining point 3 above in some additional detail. Equation (5.38) C = U Tu is, of course, not completely correct. It is only an approximation it should be written as 

The matrix C is defined by the non-linear parameters (rate constants). It is possible to minimise Ru, i.e. the corresponding ssq, as a function of these parameters in a normal Newton-Gauss algorithm. The chain of equations goes as follows 

The advantage is that there is no pseudo-inverse to be calculated in this way. The computation of Tu, which comprises linear parameters is easier than usual as U is an orthonormal matrix, U+=Ul. As mentioned before, in equation (5.29), it is advantageous to compute the residuals as Ru = C - U(Ul C) it is considerably faster. 

The standard chain of equations using Beer-Lambert s law is  

For the sake of completeness, we also include the relevant equations if data reduction, according to Reduced Eigenvector Space (p. 180), is applied  

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