Symbolic and interval rational interpolation: the problem of unattainable dataSymbolic and interval rational interpolation: the problem of unattainable data
Faculty of Sciences. Mathematics and Computer Science

Computational Mathematics

Emerging computational techniques (ECT)

article

2008New York, 2008

Mathematics

AIP conference proceedings / American Institute of Physics. - New York

1048(2008), p. 466-469

0094-243X

000259567000111

E

English (eng)

University of Antwerp

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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