Title 



A practical error formula for multivariate rational interpolation and approximation
 
Author 



 
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 wellknown 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 4dimensional example, which is only one of the several problems we tested it on.   
Language 



English
 
Source (journal) 



Numerical algorithms.  Basel  
Publication 



Basel : 2010
 
ISSN 



10171398
 
Volume/pages 



55:2/3(2010), p. 233243
 
ISI 



000281792800007
 
Full text (Publishers DOI) 


  
