Turetzkii [Uchenye Zapiski, Vypusk 1 (149) (1959), 31–55, (English translation in East J. Approx. 11 (2005) 337–359)] considered quadrature rules of interpolatory type with simple nodes, with maximal trigonometric degree of exactness. For that purpose Turetzkii made use of orthogonal trigonometric polynomials of semi–integer degree. Ghizzeti and Ossicini [Quadrature Formulae, Academie-Verlag, B...

This paper presents new univariate linear non-uniform interpolatory subdivision constructions that yield high smoothness, C and C, and are based on least-degree spline interpolants. This approach is motivated by evidence, partly presented here, that constructions based on high-degree local interpolants fail to yield satisfactory shape, especially for sparse, non-uniform samples. While this impr...

Nonlinear subdivision schemes that operate on manifolds are of use whenever manifold valued data have to be processed in a multiscale fashion. This paper considers the case where the manifold is a Lie group and the nonlinear subdivision schemes are derived from linear interpolatory ones by the so-called log-exp analogy. The main result of the paper is that a multivariate interpolatory Lie group...

In this paper a new class of interpolatory re nement schemes is presented which in every re nement step determine the new points by solving an optimization problem. In general, these schemes are global, i.e., every new point depends on all points of the polygon to be re ned. By choosing appropriate quadratic functionals to be minimized iteratively during re nement, very e cient schemes producin...

In this paper, we propose a new interpolatory subdivision scheme for generating nice-looking curvature-continuous curves of round shapes. The scheme is based on a diffusion of normals. Given a subdivided polyline, the new polyline vertices inserted at the the splitting step are updated in order to fit diffused (averaged with appropriate weights) normals. Although the resulting interpolatory sub...

This is a survey on discrete linear operators which, besides approximating in Jackson or near-best order, possess some interpolatory property at some nodes. Such operators can be useful in numerical analysis. A central problem in approximation theory is the construction of simple functions that approximate well a given set of functions. Traditionally, by “simple” we mean polynomials or rational...

We focus on interpolatory-based model order reduction for a special class of bilinear descriptor systems in the H2-optimal framework, appearing in constraint circuit simulations. The straightforward extension of the H2-optimality conditions for ODE systems to descriptor systems generically may produce an unbounded error in the H2 or H∞ norm, or both. This arises due to the inappropriate use of ...

We give a very simply computable interpolatory process, wich approximates in near-best order on [-1,1] in some Jacobi-weighted space.