Rational Interpolation: Jacobi’s Approach Reminiscence

The linear pencil approach to rational interpolation

It is possible to generalize the fruitful interaction between (real or complex) Jacobi matrices, orthogonal polynomials and Padé approximants at infinity by considering rational interpolants, (bi-)orthogonal rational functions and linear pencils zB − A of two tridiagonal matrices A, B, following Spiridonov and Zhedanov. In the present paper, beside revisiting the underlying generalized Favard t...

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 ...

A new approach to vector-valued rational interpolation

In this work we propose three different procedures for vector-valued rational interpolation of a function F(z), where F : C → C , and develop algorithms for constructing the resulting rational functions. We show that these procedures also cover the general case in which some or all points of interpolation coalesce. In particular, we show that, when all the points of interpolation collapse to th...

On Multivariate Birkhoff Rational Interpolation