Multivariate Approximation and Applications: Applied and computational aspects of nonlinear wavelet approximation

Nonlinear approximation has recently found computational applications such as data compression, statistical estimation or adaptive schemes for partial diierential or integral equations, especially through the development of wavelet-based methods. The goal of this paper is to provide with a short survey of nonlinear wavelet approximation in the perspective of these applications , as well as to stress some remaining open questions.