Abstract
One possible approach to exact real arithmetic is to use linear fractional transformations (LFTs) to represent real numbers and computations on real numbers. Recursive expressions built from LFTs are only convergent (i.e., denote a well-defined real number) if the involved LFTs are sufficiently contractive. In this paper, we define a notion of contractivity for LFTs. It is used for convergence theorems and for the analysis and improvement of algorithms for elementary functions.
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