Unrestricted Algorithms for Generating Elementary Functions
An “unrestricted” algorithm for generating a mathematical function is a computational algorithm in which the user may demand any accuracy for arguments of any magnitude. Two interesting mathematical problems arise in the construction of such algorithms for the elementary functions. First, an efficient method is needed to determine realistic a priori error bounds that is applicable when the number of arithmetical Operations is unbounded. Secondly, the free parameters associated with the algorithm need to be optimized in order to minimize the total Computing time. The first problem is solved by application of a recently-developed logarithmic form of interval analysis. The second is solved by asymptotic methods.
KeywordsWord Length Dual Form Relative Precision Conventional Definition Arbitrary Precision
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