On Hermite-Birkhoff interpolation

The Budan-fourier Theorem and Hermite-birkhoff Spline Interpolation

We extend the classical Budan-Fourier theorem to Hermite-Birkhoff splines, that is splines whose knots are determined by a finite incidence matrix. This is then applied to problems of interpolation by Hermite-Birkhoff splines, where the nodes of interpolation are also determined by a finite incidence matrix. For specified knots and nodes in a finite interval, conditions are examined under which...

Hermite Birkhoff interpolation of scattered data by combined Shepard operators

Methods approaching the problem of the Hermite Birkhoff interpolation of scattered data by combining Shepard operators with local interpolating polynomials are not new in literature [1–4]. In [3] combinations of Shepard operators with bivariate Hermite-Birkhoff local interpolating polynomials are introduced to increase the algebraic degree of precision (polynomial reproduction degree) of Shepar...

A new non-polynomial solution to multivariate Hermite-Birkhoff interpolation

A new solution to the multivariate Hermite-Birkhoff interpolation problem is presented. The classical approach to this problem consists in constructing the minimum degree polynomial, which coincides with the prescribed function and derivative values at the sample points. Here the interpolant is represented as a truncated Multipoint Taylor (MT) series. A MT series can be regarded as an extension...

Runge-Kutta Defect Control Using Hermite-Birkhoff Interpolation

Two techniques for reliably controlling the defect (residual) in the numerical solution of nonstiff initial value problems were given in [D. This work describes an alternative approach based on Hermite-Birkhoff interpolation. The new approach has two main advantagesmit is applicable to Runge-Kutta schemes of any order, and it gives rise to a defect of the optimum asymptotic order of accuracy. F...

On Multivariate Birkhoff Rational Interpolation