In this paper an overview of wavelet based multiresolution analyses is presented. First, the
continuous wavelet transform in its simplest form is discussed. Then, the definition of a …

Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and
applies methods from scientific computing to several fields including analysis, linear …

We propose simple and extremely efficient methods for solving the basis pursuit problem
\min{‖u‖_1:Au=f,u∈R^n\}, which is used in compressed sensing. Our methods are based …

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 book presents a mathematical introduction to the theory of orthogonal wavelets and
their uses in analyzing functions and function spaces, both in one and in several variables …

This note is a very basic introduction to wavelets. It starts with an orthogonal basis of
piecewise constant functions, constructed by dilation and translation. The" wavelet …

This textbook is an introduction to Scientific Computing. We will illustrate several numerical
methods for the computer solution of certain classes of mathematical problems that cannot …

This textbook is designed for graduate students in mathematics, physics, engineering, and
computer science. Its purpose is to guide the reader in exploring contemporary …

More than anything else, the increase of computing power seems to stimulate the greed for
tackling ever larger problems involving large-scale numerical simulation. As a consequence …

This survey article is concerned with two basic approximation concepts and their
interrelation with the numerical solution of elliptic operator equations, namely nonlinear and …