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

Regularization of ill-posed linear inverse problems via ℓ 1 penalization has been proposed
for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer …

Vector-valued data appearing in concrete applications often possess sparse expansions
with respect to a preassigned frame for each vector component individually. Additionally …

We propose stable variational formulations for certain linear, unsymmetric operators with first
order transport equations in bounded domains serving as the primary focus of this paper …

Abstract In [Math. Comp, 70 (2001), 27–75] and [Found. Comput. Math., 2 (3)(2002), 203–
245], Cohen, Dahmen and DeVore introduced adaptive wavelet methods for solving …

For Au= f with an elliptic differential operator A: H → H'and stochastic data f, the m-point
correlation function\mathcal M^ mu of the random solution u satisfies a deterministic …

We derive an adaptive solver for random elliptic boundary value problems, using techniques
from adaptive wavelet methods. Substituting wavelets by polynomials of the random …

This chapter offers a detailed survey on intrinsically localized frames and the corresponding
matrix representation of operators. We re-investigate the properties of localized frames and …

We provide fast and accurate adaptive algorithms for the spatial resolution of current
densities in MEG. We assume that vector components of the current densities possess a …

Matrix extension with symmetry is to find a unitary square matrix P of 2 π-periodic
trigonometric polynomials with symmetry such that the first row of P is a given row vector p of …