Recursiveness in matrix rational interpolation problems

Recursiveness in Matrix Rational Interpolation Problems 1 2

We consider the problem of computing solutions to a variety of matrix rational interpolation problems. These include the partial realization problem for matrix power series and Newton-Pad e, Hermite-Pad e, Simultaneous Pad e, M-Pad e and multipoint Pad e approximation problems along with their matrix generalizations. A general recurrence relation is given for solving these problems. Unlike othe...

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...

Monotone Rational Trigonometric Interpolation

This study is concerned with the visualization of monotone data using a piecewise C rational trigonometric interpolating scheme. Four positive shape parameters are incorporated in the structure of rational trigonometric spline. Conditions on two of these parameters are derived to attain the monotonicity of monotone data and other two are left free. Figures are used widely to exhibit that the pr...

Rational Hermite–fejér Interpolation

In this paper we construct rational orthogonal systems with respect to the normalized area measure on the unit disc. The generating system is a collection of so called elementary rational functions. In the one dimensional case an explicit formula exists for the corresponding Malmquist–Takenaka functions involving the Blaschke functions. Unfortunately, this formula has no generalization for the ...

On Multivariate Birkhoff Rational Interpolation