On the Implementation of Conceptual Algorithms
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TL;DR
This work discusses general and highly efficient procedures for implementing conceptual algorithms, i.e, for transforming them into an algorithm with iterations requiring only a finite number of function evaluations and arithmetical operations.
Abstract
For our purposes, we define an algorithm to be conceptual, if each of its iterations, when specified constructively, requires an infinite number of function evaluations and arithmetical operations. Weshall discuss general and highly efficient procedures for implementing conceptual algorithms, i.e, for transforming them into an algorithm with iterations requiring only a finite number of function evaluations and arithmetical operations. We shall discuss both adaptive and open loop methods for truncating infinite calculations.