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...

Due to properties such as interpolation, smoothness, and spline connections, Hermite subdivision schemes employ fast iterative algorithms for geometrically modeling curves/surfaces in CAGD building wavelets numerical PDEs. In this paper, we introduce a notion of generalized (dyadic) then characterize their convergence, smoothness underlying matrix masks with or without interpolation properties....

The influence of the use of the generalized Hermite polynomial on the Hermite-based lattice Boltzmann (LB) construction approach, lattice sets, the thermal weights, moments and the equilibrium distribution function (EDF) are addressed. A new moment system is proposed. The theoretical possibility to obtain a high-order Hermite-based LB model capable to exactly match some first hydrodynamic momen...

This paper discusses various aspects of Hermite-Birkhoff interpolation that involve prescibed values of a function and/or its first derivative. An algorithm is given that finds the unique polynomial that satisfies the given conditions if it exists. A mean value type error term is developed which illustrates the ill-conditioning present when trying to find a solution to a problem that is close t...

Interpolation by analytic radial basis functions like the Gaussian and inverse multiquadrics can degenerate in two ways: the radial basis functions can be scaled to become “increasingly flat”, or the data points “coalesce” in the limit while the radial basis functions stays fixed. Both cases call for a careful regularization. If carried out explicitly, this yields a preconditioning technique fo...