1 A dynamical - system analysis of the optimum s - gradient algorithm
نویسنده
چکیده
We study the asymptotic behaviour of Forsythe’s s-optimum gradient algorithm for the minimization of a quadratic function in R using a renormalization that converts the algorithm into iterations applied to a probability measure. Bounds on the performance of the algorithm (rate of convergence) are obtained through optimum design theory and the limiting behaviour of the algorithm for s = 2 is investigated into details. Algorithms that switch periodically between s = 1 and s = 2 are shown to converge much faster than when s is fixed at 2.
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A dynamical-system analysis of the optimum s-gradient algorithm
A dynamical-system analysis of the optimum s-gradient algorithm. HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée...
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