Vector valued rational interpolants over triangular grids

Algebraic properties of some new vector-valued rational interpolants

In a recent paper of the author [A. Sidi,A new approach to vector-valued rational interpolation, J.Approx. Theory, 130 (2004) 177–187], three new interpolation procedures for vector-valued functions F(z), where F : C → CN , were proposed, and some of their properties were studied. In this work, after modifying their definition slightly, we continue the study of these interpolation procedures. W...

Self-Avoiding Walks Over Adaptive Triangular Grids

In this paper, we present a new approach to constructing a "self-avoiding" walk through a triangular mesh. Unlike the popular approach of visiting mesh elements using space-filling curves which is based on a geometric embedding, our approach is combinatorial in the sense that it uses the mesh connectivity only. We present an algorithm for constructing a sell avoiding walk which can be applied t...

Polynomial Pre ision Triangular Interpolants

Vector Fitting for Matrix-valued Rational Approximation

Vector Fitting (VF) is a popular method of constructing rational approximants that provides a least squares fit to frequency response measurements. In an earlier work, we provided an analysis of VF for scalar-valued rational functions and established a connection with optimal H 2 approximation. We build on this work and extend the previous framework to include the construction of effective rati...

Convergence of Rational Interpolants∗

The convergence of (diagonal) sequences of rational interpolants to an analytic function is investigated. Problems connected with their definition are shortly discussed. Results about locally uniform convergence are reviewed. Then the convergence in capacity is studied in more detail. Here, a central place is taken by a theorem about the convergence in capacity of rational interpolants to funct...