Exact real computation in computer algebra

Authors:
Gábor Bodnár;Barbara Kaltenbacher;Petru Pau;Josef Schicho
Affiliations:
SFB Numerical and Symbolic Computation, Johannes Kepler University, Linz, Austria;SFB Numerical and Symbolic Computation, Johannes Kepler University, Linz, Austria;SFB Numerical and Symbolic Computation, Johannes Kepler University, Linz, Austria;SFB Numerical and Symbolic Computation, Johannes Kepler University, Linz, Austria
Venue:
SNSC'01 Proceedings of the 2nd international conference on Symbolic and numerical scientific computation
Year:
2001

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Abstract

Exact real computation allows many of the advantages of numerical computation (e.g. high performance) to be accessed also in symbolic computation, providing validated results. In this paper we present our approach to build a transparent and easy to use connection between the two worlds, using this paradigm. The main discussed topics are: representation of exact real objects, operations on exact real matrices, polynomial greatest common divisor and root computation. Some of these problems are ill-posed; we use regularization methods to solve them.