SET FUNCTIONS AND APPLICATIONS
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Publisher Summary A numerical algorithm cannot be carried out on a computer as there are only finitely many machine numbers. The goal of solving a problem by computing a set that necessarily contains the solution leads to the introduction of a related set arithmetic. In practice, it is important to describe such an inclusion set by finitely many numbers, and it seems profitable to use intervals of a partially ordered domain. A suitable set arithmetic, besides providing the tools for a strict execution of numerical algorithms on a computer, also offers the possibility for a general consideration and exact presentation of such algorithms. This helps to improve statements and solutions of the occurring problems. This chapter describes iteration. The motivation for the iteration procedure is the simple fact that such a method produces an always convergent, monotonic sequence.
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