On trigonometric and paratrigonometric Hermite interpolation

Trigonometric wavelets for Hermite interpolation

The aim of this paper is to investigate a multiresolution analysis of nested subspaces of trigonometric polynomials. The pair of scaling functions which span the sample spaces are fundamental functions for Hermite interpolation on a dyadic partition of nodes on the interval [0, 2π). Two wavelet functions that generate the corresponding orthogonal complementary subspaces are constructed so as to...

Hermite Interpolation Using ERBS with Trigonometric Polynomial Local Functions

Constrained Interpolation via Cubic Hermite Splines

Introduction In industrial designing and manufacturing, it is often required to generate a smooth function approximating a given set of data which preserves certain shape properties of the data such as positivity, monotonicity, or convexity, that is, a smooth shape preserving approximation.  It is assumed here that the data is sufficiently accurate to warrant interpolation, rather than least ...

Means and Hermite Interpolation

Let m2 < m1 be two given nonnegative integers with n = m1+m2+1. For suitably differentiable f , we let P,Q ∈ πn be the Hermite polynomial interpolants to f which satisfy P (a) = f (a), j = 0, 1, ..., m1 and P (b) = f (b), j = 0, 1, ..., m2, Q (a) = f (a), j = 0, 1, ..., m2 and Q(b) = f (b), j = 0, 1, ..., m1. Suppose that f ∈ C (I) with f (x) 6= 0 for x ∈ (a, b). If m1 − m2 is even, then there ...

Algebraic-Trigonometric Pythagorean-Hodograph curves and their use for Hermite interpolation

In this article we define a new class of Pythagorean-Hodograph curves built-upon a sixdimensional mixed algebraic-trigonometric space, we show their fundamental properties and compare them with their well-known quintic polynomial counterpart. A complex representation for these curves is introduced and constructive approaches are provided to solve different application problems, such as interpol...