The Finite Termination Property of an Algorithm for Solving the Minimum Circumscribed Ball Problem

In this paper basic mathematical tasks of coordinate measurement are briefly described and a modified 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 simplified step size rule and finds the solution of the minimum circumscribed ball fitting after only a finite number The iteration is of the steepest descent type applied to the related distance function. But, in contrast to standard algorithms it uses a modified step size rule that takes into account the specific properties of the occurring objective function. This small difference in the code improves the performance of the algorithm and it enables real time use of the proposed method in coordinate measurement machines. The effciency of the prosed algorithm will be illustrated by some typical examples.