Generalized bivariate Hermite fractal interpolation function

Error bounds for bivariate piecewise hermite interpolation

Unique Solvability in Bivariate Hermite Interpolation

We consider the question of unique solvability in the context of bivariate Hermite interpolation. Starting from arbitrary nodes, we prescribe arbitrary conditions of Hermite type, and find an appropriate interpolation space in which the problem has a unique solution. We show that the coefficient matrix of the associated linear system is a nonsingular submatrix of a generalized Kronecker product...

Case study in bivariate Hermite interpolation

In this article we investigate the minimal dimension of a subspace of C1(R2) needed to interpolate an arbitrary function and some of its prescribed partial derivatives at two arbitrary points. The subspace in question may depend on the derivatives, but not on the location of the points. Several results of this type are known for Lagrange interpolation. As far as I know, this is the first such s...

Generalization of Hermite functions by fractal interpolation

Fractal interpolation techniques provide good deterministic representations of complex phenomena. This paper approaches the Hermite interpolation using fractal procedures. This problem prescribes at each support abscissa not only the value of a function but also its first p derivatives. It is shown here that the proposed fractal interpolation function and its first p derivatives are good approx...

Hidden Variable Bivariate Fractal Interpolation Surfaces

We construct hidden variable bivariate fractal interpolation surfaces (FIS). The vector valued iterated function system (IFS) is constructed in R and its projection in R is taken. The extra degree of freedom coming from R provides hidden variable, which is an important factor for flexibility and diversity in the interpolated surface. In the present paper, we construct an IFS that generates both...