Wednesday, 18 July 2018

AREA UNDER THE CURVE AND LINEAR PROGRAMING NOTE BY PLANCESS

The technique of linear programming is a very powerful and widely applied numerical method. In general, chemists have not made use of this tool. Here we present a simple example which shows the superiority of a linear programming based fitting process over that of the weighted or unweighted least squares formulation. 

In addition the example shows the simultaneous use of more than one method for determining the dependent variable. Specifically, the example we have chosen is the fitting of single exponential relaxation curves. When applied to data which has varying amounts of random noise added to it, the linear programming technique proves quite consistently to be more accurate than the common unweighted least squares formulation or the weighted least squares technique. Some of this improvement can be credited to the use of the area under the relaxation curve as a constant on the determined relaxation time.

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