We construct bounded polynomial operators, similar to the classical de la Valleé Poussin operators in Fourier series, which preserve polynomials of a certain degree, but are defined in terms of the values of the function rather than its Fourier coefficients. AMS classification: 41 A 10, 41 A 05

We present a new approach to the construction of biorthogonal wavelet transforms using polynomial splines. The construction is performed in a “lifting” manner and we use interpolatory, as well as local quasi-interpolatory and smoothing splines as predicting aggregates in this scheme. The transforms contain some scalar control parameters which enable their flexible tuning in either time or frequ...

Given a dilation matrix A : Z d → Z d , and G a complete set of coset representatives of 2π(A −− Z d /Z d), we consider polynomial solutions M to the equation g∈G M (ξ + g) = 1 with the constraints that M ≥ 0 and M (0) = 1. We prove that the full class of such functions can be generated using polynomial convolution kernels. Trigonometric polynomials of this type play an important role as symbol...

This short note presents four examples of compactly supported symmetric refinable componentwise polynomial functions: (i) a componentwise constant interpolatory continuous refinable function and its derived symmetric tight wavelet frame; (ii) a componentwise constant continuous orthonormal and interpolatory refinable function and its associated symmetric orthonormal wavelet basis; (iii) a diffe...

We consider model order reduction of bilinear descriptor systems using an interpolatory projection framework. Such nonlinear descriptor systems can be represented by a series of generalized linear descriptor systems (also called subsystems) by utilizing the Volterra-Wiener approach [22]. Standard projection techniques for bilinear systems utilize the generalized transfer function of these subsy...

A generic technique for construction of ternary interpolatory subdivision schemes, which is based on polynomial and discrete splines, is presented. These schemes have rational symbols. The symbols are explicitly presented in the paper. This is accompanied by a detailed description of the design of the refinement masks and by algorithms that verify the convergence of these schemes. In addition, ...

This paper uses some well known theorems of algebraic geometry to characterize polynomial Hermite interpolation in any dimension. Efficient numerical algorithms are presented for interpolatory curve fits through points in the plane, surface fits through points and curves in space, and in general, hypersuface fits through. points, curves, surfaces, and sub-varieties in n dimensional space. These...

We discuss whether or not it is possible to have interpolatory pointwise estimates in the approximation of a function f 2 C 0; 1], by polynomials. For the sake of completeness as well as in order to strengthen some existing results, we discuss brieey the situation in unconstrained approximation. Then we deal with positive and monotone constraints where we show exactly when such interpolatory es...

In this paper we describe a general, computationally feasible strategy to deduce a family of interpolatory non-stationary subdivision schemes from a symmetric non-stationary, non-interpolatory one satisfying quite mild assumptions. To achieve this result we extend our previous work [C. Conti, L. Gemignani, L. Romani, Linear Algebra Appl. 431 (2009), no. 10, 1971– 1987] to full generality by rem...