MEGA 2007 Effective Methods in Algebraic Geometry Strobl, Austria, June 25th - 29th http://www.ricam.oeaw.ac.at/mega2007

Abstract

Title	Twin-Float Arithmetic
Keywords	floating-point approximation
Abstract	We present a heuristically certified form of floating-point arithmetic. As prerequisite we need floating-point arithmetic where the user can set the precision. Our work is developed from the idea of paired floats expounded by Traverso and Zanoni [2]. Twin-float arithmetic is suitable for use only where the input data are exact (or can be obtained to high enough precision). The arithmetic includes a (heuristic) zero test, and so can be used in Buchberger's Algorithm. The ideas presented here are implemented as a ring in CoCoALib, called RingFloat, allowing them to be used in a wide variety of algebraic computations including Groebner bases.

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