Local least squares algorithm

The parameters of the baseline are automatically modified only if the Leven-berg—Marquardt algorithm is used. If the Local Least Squares algorithm is selected, the parameters are set manually. 

The Local Least Squares algorithm performs an independent fit for each individual peak. The calculation is thereby restricted to the range around the band maximum. This drastically reduces the amount of data required for the calculation, enhancing the speed compared to the Levenberg-Marquardt method. Some loss of precision versus the Levenberg-Marquardt method occurs. The Local Least Squares algorithm has some conditions ... 

With least-squares (LS) algorithms for non-linear problems such as multiway methods, the problem of local minima solutions6 is well known and it is common practice to repeat the calculation a number of times using different starting estimates for the components. This way the results of several models are compared and if the calculated models are sufficiently similar, it is likely that the global LS minimum has been found, whereas if the models are dissimilar, local LS minima are likely to be present. In case of local LS minima, more repetitions can be made in order to see if a consistent pattern... 

Apart from the original method mentioned above, Morrison and eo-workers [143,144] formulated a new iterative teehnique ealled CAEDMON (Computed Adsorption Energy Distribution in the Monolayer) for the evaluation of the energy distribution from adsorption data without any a priori assumption about the shape of this function. In this case, the local adsorption is calculated numerically from the two-dimensional virial equation. The problem is to find a discrete distribution function that gives the best agreement between the experimental data and calculated isotherms. In this order, the optimization procedure devised for the solution of non-negative constrained least-squares problems is used [145]. The CAEDMON algorithm was applied to evaluate x(fi) for several adsorption systems [137,140,146,147]. Wesson et al. [147] used this procedure to estimate the specific surface area of adsorbents. 

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