Osculatory Interpolation

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 •<* ...

Bivariate Blending Thiele-Werner’s Osculatory Rational Interpolation

Optimum-Point Formulas for Osculatory and Hyperosculatory Interpolation

Formulas are given for n-point osculatory and hyperosculatory (as well as ordinary) polynomial interpolation for f(x), over ( —1, 1), in terms of fixi), f'(xi) and f"(x/) at the irregularly-spaced Chebyshev points x¡ = —cos {(2i — l)ir/2n}, i = 1, • • ■ , n. The advantage over corresponding formulas for Xi equally spaced is in the squaring and cubing, in the respective osculatory and hyperoscul...

A note on cubic convolution interpolation

We establish a link between classical osculatory interpolation and modern convolution-based interpolation and use it to show that two well-known cubic convolution schemes are formally equivalent to two osculatory interpolation schemes proposed in the actuarial literature about a century ago. We also discuss computational differences and give examples of other cubic interpolation schemes not pre...

On the osculatory behaviour of higher dimensional projective varieties

Here we explore the geometry of the osculating spaces to projective varieties of arbitrary dimension. In particular, we classify varieties having very degenerate higher order osculating spaces and we determine mild conditions for the existence of inflectionary points. AMS Subject Classification: 14N05.