Optimization of the Model Curve Fitting

Once a mathematical model has been ehosen, there is the option of either fixing certain parameters (see Section 4.10) or fixing certain points, e.g., constraining the calibration line to go through the origin. 3- ,74,ii3 

When one tries to fit a mathematical function to a set of data one has to choose a method or algorithm for achieving this end, and choose a weighting model with which to judge the goodnss of fit. 

Each of these four classes has its particular advantages. 

The algebraic solution is the classical fitting technique, as exemplified by the linear regression (Chapter 2). The advantage lies in the clear formulation of the numerical algorithm to be used and in the uniqueness of the solution. If one is free to choose the calibration concentrations and the number of 

Ok) function is sought by repeatedly determining the direction of steepest descent (maximum change in for any change in the coefficients a,), and taking a step to establish a new vertex. A numerical example is found in Table 1.26. An example of how the simplex method is used in optimization work is given in Ref. 143. 

The algebraic/iterative and the brute force methods are numerical respectively computational techniques that operate on the chosen mathematical model. Raw residuals r are weighted to reflect the relative reliabilities of the measurements. 

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OPTIMIZATION TECHNIQUES 3.5.3 Optimization of the Model Curve Fitting... 

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