Multivariate rational data fitting: general data structure,maximal accuracy and object orientation

Sections 1 and 2 discuss the advantages of an object-oriented implementation combined with higher floating-point arithmetic, of the algorithms available for multivariate data fitting using rational functions. Section 1 will in particular explain what we mean by higher arithmetic. Section 2 will concentrate on the concepts of object orientation. In sections 3 and 4 we shall describe the generality of the data structure that can be dealt with: due to some new results virtually every data set is acceptable right now, with possible coalescence of coordinates or points. In order to solve the multivariate rational interpolation problem the data sets are fed to different algorithms depending on the structure of the interpolation points in then-variate space.This text is a preparatory publication for the development of a scientific expert system for multivariate rational interpolation. The issues addressed are relevant to the implementation of such a system.