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Second Conference on Numerical Analysis and Applications
June 11-15, 2000
University of Rousse
Rousse, Bulgaria |
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Organizers
Plamen Yalamov, Marcin Paprzycki, Lubin Vulkov
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From sensitivity analysis to random floating point arithmetics ...
by
Alain Barraud
Laboratoire d'Automatique de Grenoble, INPG, France
Coauthors: Suzanne Lesecq, Nicolai Christov
Alain Barraud, Suzanne Lesecq, Nicolai Christov
Laboratoire d'Automatique de Grenoble, BP46
F-38402 Saint Martin d'Hères
Alain.Barraud@inpg.fr, Suzanne.Lesecq@inpg.fr, Nicolai.Christov@inpg.fr
From sensitivity analysis to random floating point arithmetics. Application
to Sylvester equations
From sensitivity analysis to random floating point arithmetics. Application
to Sylvester equations
28 January 2000
ABSTRACT
Numerical problem solving is a basic approach in many scientific
applications. Potential ill conditioning of the problem is always the
background question about the computed results accuracy. Accessing the
solver precision may be much more difficult than solving a given problem. In
this paper two alternative approaches for the precision estimation are
analyzed: an indirect precision estimation via condition number computation,
and a direct technique based upon random arithmetic. Sylvester equations are
used as a comparison support because a complete sensitivity analysis is
available for them, true (structured) condition numbers can be computed and
robust software exists for solving purpose. Some basic results are given in
the paper concerning the perturbation analysis and structured Sylvester
condition numbers. An oriented accessing precision random arithmetic
theoretical background is presented in detail. This technique is
fundamentally component wise, and not global as condition numbers are.
Furthermore, a Matlab implementation is described as a new object class
which overloads most of the available operators and commands. It makes
possible the already existing Matlab solvers to perform as they usually do
and the results precision to be available everywhere. Performance
comparisons are presented and analyzed. The conclusions show why and how
this approach is basically generic, compared with traditional condition
number estimation.
Keywords: Condition numbers, Accuracy estimation, Random
arithmetics, Pertubation analysis, Sylvester equations
Date received: January 31, 2000
Copyright © 2000 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # caeb-49.