Title
Symbolic and interval rational interpolation: the problem of unattainable data Symbolic and interval rational interpolation: the problem of unattainable data
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
New York ,
Subject
Mathematics
Source (journal)
AIP conference proceedings / American Institute of Physics. - New York
Volume/pages
1048(2008) , p. 466-469
ISSN
0094-243X
ISI
000259567000111
Carrier
E
Target language
English (eng)
Affiliation
University of Antwerp
Abstract
A typical problem with rational interpolation is that of a so-called unattainable point, when the interpolation condition cannot be met by the rational interpolant of the specified degree. The problem can be dealt with in at least two approaches, one of which is novel and practically oriented. We admit infinity in the independent variable as well as in the function value. Rational interpolation is solved symbolically in its full generality by Van Barel and Bultheel [9]. The authors return a parameterized set of rational interpolants of higher degree than requested but without unattainable points. In many practical applications however, observations are not exact but prone to imprecise measurements. A natural way for dealing with uncertainty in the data is by means of an uncertainty interval. It is shown in [1] how a rational function of lowest complexity can be obtained which intersects all uncertainty intervals and avoids the typical problem of unattainable data.
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