On bivariate osculatory interpolation

Bivariate Blending Thiele-Werner’s Osculatory Rational 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 mean value interpolation on circles of the same radius

We consider   bivariate  mean-value interpolationproblem, where the integrals over circles are interpolation data. In this case the problem  is described  over   circles of the same radius and with  centers are on astraight line and it is shown that in this case the interpolation is not correct.

Bivariate interpolation based on univariate subdivision schemes

The paper presents a bivariate subdivision scheme interpolating data consisting of univariate functions along equidistant parallel lines by repeated refinements. This method can be applied to the construction of a surface passing through a given set of parametric curves. Following the methodology of polysplines and tension surfaces, we define a local interpolator of four consecutive univariate ...

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...