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.

The objective of this paper is to introduce a general procedure for deriving interpolatory surface subdivision schemes with “symmetric subdivision templates” (SSTs) for regular vertices. While the precise definition of “symmetry” will be clarified in the paper, the property of SSTs is instrumental to facilitate application of the standard procedure for finding symmetric weights for taking weigh...

We discuss whether on not it is possible to have interpolatory estimates in the approximation of a function Sobolev`s space by polynomials. The prob-lem positive estimate pointwise degree approxi-mation r times continuously differentiable and func-tions [0, 1]. Estimates form (1) for are known ([1, 2]). problem monotone that estimating de-gree nondecreasing bymonotone were proved [3, 4, 7]. In ...

The last two decades have seen major developments in interpolatory methods for model reduction of large-scale linear dynamical systems. Advances of note include the ability to produce (locally) optimal reduced models at modest cost; refined methods for deriving interpolatory reduced models directly from input/output measurements; and extensions for the reduction of parametrized systems. This ch...

We find a family of convergent schemes nodes for non-complete interpolatory quadrature rules.

This paper is devoted to a study of interpolatory refinable functions. If a refinable function φ on Rs is continuous and fundamental, i.e., φ(0) = 1 and φ(α) = 0 for α ∈ Zs\{0}, then its corresponding mask b satisfies b(0) = 1 and b(2α) = 0 for all α ∈ Zs\{0}. Such a refinement mask is called an interpolatory mask. We establish the existence and uniqueness of interpolatory masks which are induc...

The convergence of the minimal energy interpolatory splines on the unit sphere is studied in this paper. An upper bound on the difference between a sufficiently smooth function and its interpolatory spherical spline in the infinity norm is given. The error bound is expressed in terms of a second order spherical Sobolev-type seminorm of the original function. §