Unattainable Points in Multivariate Rational Interpolation

On Multivariate Birkhoff Rational Interpolation

Rational Interpolation at Chebyshev points

The Lanczos method and its variants can be used to solve eeciently the rational interpolation problem. In this paper we present a suitable fast modiication of a general look-ahed version of the Lanczos process in order to deal with polynomials expressed in the Chebyshev orthogonal basis. The proposed approach is particularly suited for rational interpolation at Chebyshev points, that is, at the...

Multivariate Rational Interpolation of Scattered Data

Abstract. Rational data fitting has proved extremely useful in a number of scientific applications. We refer among others to the computation of cell loss probabilities in network traffic [5, 6, 14, 15], to the modelling of electro-magnetic components [20, 12] to model reduction of linear shift-invariant systems [2, 3, 7] and so on. When computing a rational interpolant in one variable, all exis...

Sparse interpolation of multivariate rational functions

Consider the black box interpolation of a τ -sparse, n-variate rational function f , where τ is the maximum number of terms in either numerator or denominator. When numerator and denominator are at most of degree d, then the number of possible terms in f is O(dn) and explodes exponentially as the number of variables increases. The complexity of our sparse rational interpolation algorithm does n...

Matrix Rational Interpolation with Poles as Interpolation Points

In this paper, we show the equivalence between matrix rational interpolation problems with poles as interpolation points and no-pole problems. This equivalence provides an effective method for computing matrix rational interpolants having poles as interpolation points. However, this equivalence is only valid in those cases where enough pole information is known. It is an open problem on how one...