Title
A practical error formula for multivariate rational interpolation and approximation A practical error formula for multivariate rational interpolation and approximation
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Basel ,
Subject
Mathematics
Computer. Automation
Source (journal)
Numerical algorithms. - Basel
Volume/pages
55(2010) :2/3 , p. 233-243
ISSN
1017-1398
ISI
000281792800007
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
We consider exact and approximate multivariate interpolation of a function f(x 1 , . . . , x d ) by a rational function p n,m /q n,m (x 1 , . . . , x d ) and develop an error formula for the difference f − p n,m /q n,m . The similarity with a well-known univariate formula for the error in rational interpolation is striking. Exact interpolation is through point values for f and approximate interpolation is through intervals bounding f. The latter allows for some measurement error on the function values, which is controlled and limited by the nature of the interval data. To achieve this result we make use of an error formula obtained for multivariate polynomial interpolation, which we first present in a more general form. The practical usefulness of the error formula in multivariate rational interpolation is illustrated by means of a 4-dimensional example, which is only one of the several problems we tested it on.
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