The Mathemagix project aims at the development of a “computer analysis” system, in which numerical computations can be done in a mathematically sound manner. A major challenge for such systems is to conceive algorithms which are both efficient, reliable and available at any working precision. In this paper, we survey several older and newer such algorithms. We mainly concentrate on the automatic and efficient computation of high quality error bounds, based on a variant of interval arithmetic which we like to call “ball arithmetic”.

Keywords: ball arithmetic, interval arithmetic, reliable computing, computable analysis

A.M.S. subject classification: 65G20, 03F60, 65F99, 37-04

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Corrected version: Pdf-2018