Sparse interpolation of multivariate rational functions

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...

Interpolation of Sparse Rational Functions Without Knowing Bounds on Exponents

We present the first algorithm for the (black box) interpolation of t-sparse, n-variate rational functions without knowing bounds on exponents of their sparse representation with the number of queries independent on exponents. In fact, the algorithm uses O(ntt) queries to the black box, and can be implemented for a fixed t in a polynomially bounded storage (or polynomial parallel time). natural...

On Multivariate Birkhoff Rational Interpolation

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...

Computational Complexity of Sparse Rational Interpolation

We analyse the computational complexity of sparse rational interpolation, and give the first deterministic algorithm for this problem with singly exponential bounds on the number of arithmetic operations. A preliminary version of this paper has appeared in [10] The first author would like to thank the Max Planck Institute in Bonn for its hospitality and support during the preparation of this pa...