In the present paper, we give a survey of the recent results and outline future prospects of
the tensor-structured numerical methods in applications to multidimensional problems in …

Over the last decade several constructions of compactly supported wavelets originated both
from mathematical analysis and the signat processing community. The roots of critically …

We present the lifting scheme, a simple construction of second generation wavelets; these
are wavelets that are not necessarily translates and dilates of one fixed function. Such …

This article is essentially tutorial in nature. We show how any discrete wavelet transform or
two band subband filtering with finite filters can be decomposed into a finite sequence of …

We present the lifting scheme, a new idea for constructing compactly supported wavelets
with compactly supported duals. The lifting scheme uses a simple relationship between all …

Wavelets have proven to be powerful bases for use in numerical analysis and signal
processing. Their power lies in the fact that they only require a small number of coefficients …

This paper is concerned with the construction and analysis of wavelet-based adaptive
algorithms for the numerical solution of elliptic equations. These algorithms approximate the …

In the present paper, we discuss the novel concept of super-compressed tensor-structured
data formats in high-dimensional applications. We describe the multifolding or quantics …

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 …

Hierarchical matrices present an efficient way of treating dense matrices that arise in the
context of integral equations, elliptic partial differential equations, and control theory. While a …