Title 



Multivariate rational interpolation of scattered data
 
Author 



 
Abstract 



Rational data fitting has proved extremely useful in a number of scientific applications. We refer among others to its use in some network problems [6, 7, 15, 16], to the modelling of electromagnetic components [20,13], to model reduction of linear shiftinvariant systems [2, 3,8] and so on. When computing a rational interpolant in one variable, all existing techniques deliver the same rational function, because all rational functions that satisfy the interpolation conditions reduce to the same unique irreducible form. When switching from one to many variables, the situation is entirely different. Not only does one have a large choice of multivariate rational functions, but moreover, different algorithms yield different rational interpolants and apply to different situations. The rational interpolation of function values that are given at a set of points lying on a multidimensional grid, has extensively been dealt with in [11, 10, 5]. The case where the interpolation data are scattered in the multivariate space, is far less discussed and is the subject of this paper. We present a fast solver for the linear block CauchyVandermonde system that translates the interpolation conditions, and combine it with an interval arithmetic verification step. 
 
Language 



English
 
Source (journal) 



Lecture notes in computer science.  Berlin, 1973, currens  
Publication 



Berlin : 2004
 
ISSN 



03029743 [print]
16113349 [online]
 
Volume/pages 



2907(2004), p. 204213
 
ISI 



000189446500022
 
