On two-variable rational interpolation

Rational Interpolation and State Variable Realizations

ABSTILACT: The problem is considered of passing from interpolation data for a real rational trarlsfer function matrix to a ~ninintal skate variable realization of the transfer function matrix. The tool is a Loewner matrix, which is a generalization of the standard Mankel matrix of linear s y s tetn realization theory, and which possesses a decompositioil into a product of generalized observabil...

On Multivariate Birkhoff Rational Interpolation

On the Problem of Stable Rational Interpolation

Aspects of the stability issue in connection with rational interpolation are investigated. In particular, it is shown that unconstrained interpolation of a given set of points together with an associated mirror-image set of points yields a one-parameter family of stable interpolating functions. As an application, it is also shown that if a certain number of Markov parameters are given, by appro...

On the Osculatory Rational Interpolation Problem

The problem of the existence and construction of a table of osculating rational functins fj m for 1, m > 0 is considered. First, a survey is given of some results from the theory of osculatory rational interpolation of order s¡ — 1 at points x¡ for i > 0. Using these results, we prove the existence of continued fractions of the form c0 + c, -(x y0) + . . . + ck-(x y0) . . . (x yk_x) ck + l •<* ...

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...