Abstract
Computer-based metrology now makes use of exchange algorithms for computing best-fit geometries in which the solution is obtained by a series of iterations each involving the exchange of one previously unused data point for one of the dominant points of the previous iteration according to formal rules. While conferring large advantages in specific circumstances, their major significance is that of being examples of a class of optimization of much wider applicability.
This paper examines the theoretical basis of these algorithms in linear programming and develops a general approach to the solution of this class from which new applications can be derived. To maintain an engineering context in the analysis, practical examples are used, mainly from the field of roundness measurement.
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