Publisher Summary This chapter explains basic examples of wavelet methods in numerical
analysis. It introduces the approximations and shows show the way they are related to …

Meshfree approximation methods are a relatively new area of research, and there are only a
few books covering it at present. Whereas other works focus almost entirely on theoretical …

This paper presents an account of the current state of sampling, 50 years after Shannon's
formulation of the sampling theorem. The emphasis is on regular sampling, where the grid is …

This is a survey of nonlinear approximation, especially that part of the subject which is
important in numerical computation. Nonlinear approximation means that the approximants …

This paper presents a chronological overview of the developments in interpolation theory,
from the earliest times to the present date. It brings out the connections between the results …

We discuss wavelet frames constructed via multiresolution analysis (MRA), with emphasis
on tight wavelet frames. In particular, we establish general principles and specific algorithms …

Consider the problem of sampling signals which are not bandlimited, but still have a finite
number of degrees of freedom per unit of time, such as, for example, nonuniform splines or …

Compactly supported smooth piecewise polynomial functions provide an efficient tool for the
approximation of curves and surfaces and other smooth functions of one and several …

We present a general approach to a module frame theory in C*-algebras and Hilbert C*-
modules. The investigations rely on the ideas of geometric dilation to standard Hilbert C …

A simple characterization is given of finitely generated subspaces of L 2 (R d) which are
invariant under translation by any (multi) integer, and is used to give conditions under which …