Optical EngineeringRefined simplex fitting method
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The simplex fitting method makes use of a geometrical figure that finds the minimum variance value in successive steps. It was developed from the idea of finding the minimum value of a function. A set of vertices are assigned at first with associated coefficients and variances. The vertex with the highest variance value moves by one of the four mechanisms of reflection, expansion, contraction, or shrinkage. By repeating this process, the vertices proceed toward the minimum value of variance. Finally, the best fit to the basis function is achieved, and appropriate coefficients can be derived. When the algorithm of the simplex fitting method was examined, it was found that one of the four mechanisms, shrinkage, may not be used normally for continuous functions. This was also confirmed by examining the usage of the mechanism in the fitting of several equations. A revised flowchart of the simplex fitting method is presented.