The Finite Termination Property of an Algorithm for Solving the Minimum Circumscribed Ball Problem
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In this paper basic mathematical tasks of coordinate measurement are briefly described and a modied optimization algorithm is proposed. Coordinate measurement devices generate huge data set and require adapted methods to solve related mathematical problems in real time. The proposed algorithm possesses a simplied step size rule and nds the solution of the minimum circumscribed ball fitting after only a nite number The iteration is of the steepest descent type applied to the related distance function. But, in contrast to standard algorithms it uses a modied step size rule that takes into account the specic properties of the occurring objective function. This small dierence in the code improves the performance of the algorithm and it enables real time use of the proposed method in coordinate measurement machines. The eciency of the prosed algorithm will be illustrated by some typical examples.
21 - 05 - 2015
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