On uniform approximation with interpolatory constraints

Approximation with Interpolatory Constraints

Given a triangular array of points on [−1, 1] satisfying certain minimal separation conditions, a classical theorem of Szabados asserts the existence of polynomial operators that provide interpolation at these points as well as a near-optimal degree of approximation for arbitrary continuous functions on the interval. This paper provides a simple, functional-analytic proof of this fact. This abs...

Interpolatory Subdivision with Shape Constraints for Curves ∗

We derive two reformulations of the C1 Hermite subdivision scheme introduced by Merrien. One where we separate computation of values and derivatives and one based of refinement of a control polygon. We show that the latter leads to a subdivision matrix which is totally positive. Based on this we give algorithms for constructing subdivision curves that preserve positivity, monotonicity, and conv...

Non-uniform interpolatory subdivision via splines

We present a framework for deriving non-uniform interpolatory subdivision algorithms closely related to non-uniform spline interpolants. Families of symmetric non-uniform interpolatory 2n-point schemes of smoothness C are presented for n = 2, 3, 4 and even higher order, as well as a variety of non-uniform 6-point schemes with C continuity.

On Constrained Uniform Approximation

Polynomial-based non-uniform interpolatory subdivision with features control

Starting from a well-known construction of polynomial-based interpolatory 4-point schemes, in this paper we present an original affine combination of quadratic polynomial samples that leads to a non-uniform 4-point scheme with edge parameters. This blending-type formulation is then further generalized to provide a powerful subdivision algorithm that combines the fairing curve of a non-uniform r...