Halting the Simplex

The convergence time of the super-modified simplex was found experimentally to be proportional to the training set size and proportional to the square of the number of dimensions C2423. 

The simplex method was originally proposed by Spendley, Next, and Himsworth C4353 in 1962 and modified by Nelder and Mead C4253 in 1965. The simplex optimization has been successfully applied to several areas of analytical chemistry such as experimental optimization C189, 4143, data reduction C4263 and instrument control C4153. 

Appli cations of the simplex method in pattern recogni t i on were examined by Isenhour, Wilkins et. al. for the interpretation of mass spectra C137, 165, 242, 2433, and carbon-13 nuclear magnetic resonance spectra C26, 273. 

The application of pattern recognition to the recognition of chemical substructures on the basis of mass spectra did not reveal considerable advantages of the super-modified simplex over the modified simplex C1373. Extensive examinations of the behaviour of the simplex algorithm in pattern recognition have been made with artificial data C2423. 

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