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For evaluation of arithmetical expressions using multiple precision floating-point arithmetic, a method is given to automatically perform error cumulation control prior to the actual computations. Individual errors and their effects are identified, and it is shown how to compute these effects efficiently via automatic differentiation. In the presented approach these effects we used to determine which precisions have to be chosen during the real computations, in order to limit error cumulation to admissible, user chosen error bounds.

An improved approach to automatic error cumulation control