Integral equation formulations are a competitive strategy in computational electromagnetics
but, lamentably, are often plagued by ill-conditioning and by related numerical instabilities …

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 …

This paper introduces a new class of bases, called bandelet bases, which decompose the
image along multiscale vectors that are elongated in the direction of a geometric flow. This …

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 …

With respect to space-time tensor-product wavelet bases, parabolic initial boundary value
problems are equivalently formulated as bi-infinite matrix problems. Adaptive wavelet …

Wavelets have emerged as an important tool in analyzing functions containing
discontinuities and sharp spikes. They were developed independently in the fields of …

This paper is concerned with the design and analysis of adaptive wavelet methods for
systems of operator equations. Its main accomplishment is to extend the range of …

The efficient treatment of dense matrices arising, eg, from the finite element discretisation of
integral operators requires special compression techniques. In this article we use the-matrix …

This paper describes the construction of second generation bandelet bases and their
application to 3D geometry compression. This new coding scheme is orthogonal and the …