In the present paper polynomial interpolating scaling function and wavelets are constructed by using the interpolation properties of de la Vallée Poussin kernels with respect to the four kinds of Chebyshev weights. For the decomposition and reconstruction of a given function efficient algorithms based on fast discrete cosine and sine transforms are proposed.

Interpolating scalar refinable functions with compact support are of interest in several applications such as sampling theory, signal processing, computer graphics, and numerical algorithms. In this paper, we shall generalize the notion of interpolating scalar refinable functions to compactly supported interpolating d-refinable function vectors with any multiplicity r and dilation factor d. Mor...

Multiresolution analysis in Quantum Chemistry provide e cient computational methods. In this article, we propose several representations of the Hamiltonian operator arising from the Density Functional Theory, based on orthogonal and interpolating scaling function bases. These high order approximations allows to compute the potential and kinetic energies with a linear complexity. Finally numeric...

In this paper we consider two non–linear generalizations of such fractal interpolating functions. The first concerns how to extend the linear interpolation of Eq. (4) to higher–degree interpolations. The second generalization arises when one considers the construction of fractal interpolating functions for functions of two (or more) variables – here, even a linear interpolation of the form of E...