We construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity. The order of regularity increases linearly with the support width. We start by reviewing the conceptâ€¦ (More)

The typical paradigm for obtaining a compressed version of a discrete signal represented by a vector x âˆˆ R is to choose an appropriate basis, compute the coefficients of x in this basis, and thenâ€¦ (More)

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 solution u of theâ€¦ (More)

Orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide. We show here that underâ€¦ (More)

The use of multiresolution decompositions in the context of finite volume schemes for conservation laws was first proposed by A. Harten for the purpose of accelerating the evaluation of numericalâ€¦ (More)

We consider the problem of approximating a given element f from a Hilbert space H by means of greedy algorithms and the application of such procedures to the regression problem in statisticalâ€¦ (More)

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 applicability of the adaptiveâ€¦ (More)

Parametric partial differential equations are commonly used to model physical systems. They also arise when Wiener chaos expansions are used as an alternative to Monte Carlo when solving stochasticâ€¦ (More)

Deterministic Galerkin approximations of a class of second order elliptic PDEs with random coefficients on a bounded domain D âŠ‚ R are introduced and their convergence rates are estimated. Theâ€¦ (More)