Contractivity of Linear Fractional Transformations

Reinhold Heckmann


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

Key words: Exact Real Arithmetic, Linear Fractional Transformations

[ (15p, 60k)]

Reinhold Heckmann /