Given a set of scattered data with derivatives values, we use a minimal energy method to find Hermite interpolation based on bivariate spline spaces over a triangulation of the scattered data locations. We show that the minimal energy method produces a unique Hermite spline interpolation of the given scattered data with derivative values. Also we show that the Hermite spline interpolation conve...

By using the algorithm of Nfimberger and Riessinger (1995), we construct Hermite interpolation sets for spaces of bivariate splines Sq(d 1 ) of arbitrary smoothness defined on the uniform type triangulations. It is shown that our Hermite interpolation method yields optimal approximation order for q >~ 3.5r + 1. In order to prove this, we use the concept of weak interpolation and arguments of Bi...

A threshold scheme, which is introduced by Shamir in 1979, is very famous as a secret sharing scheme. Dealer distribute shares of a secret value among n participants. Gathering t(≤ n) participants, a secret value can be reconstructed. This is called a (t, n) secret sharing scheme. This scheme is based on Lagrange’s interpolation formula. As regard interpolation formula, it is known not only Lag...

We derive the generalized Hermite interpolation by using the contour integral and extend the generalized Hermite interpolation to obtain the sampling expansion involving derivatives for band-limited functions f , that is, f is an entire function satisfying the following growth condition |f(z)| ≤ A exp(σ|y|) for some A, σ > 0 and any z = x + iy ∈ C.

We introduce and discuss a new computational model for Hermite–Lagrange interpolation by nonlinear classes of polynomial interpolants. We distinguish between an interpolation problem and an algorithm that solves it. Our model includes also coalescence phenomena and captures a large variety of known Lagrange-Hermite interpolation problems and algorithms. Like in traditional Hermite–Lagrange inte...

Hermite interpolation is shown to be much more stable than Nyström interpolation in the context of solving classic Fredholm second kind integral equations of potential theory in two dimensions using panel-based Nyström discretization. AMS subject classification (2000): 31A10,45B05,65D05,65R20.