An approach for the construction of optimal analog wavelet bases is presented. First, the definition of an analog wavelet is given. Based on the definition and the least-squares error criterion, a general framework for designing optimal analog wavelet bases is established, which is one of difficult nonlinear constrained optimization problems. Then, to solve this problem, a hybrid algorithm by c...

In this paper we construct a class of locally supported wavelet bases for C Lagrange nite element spaces on possibly non uniform meshes on n dimensional domains or manifolds The wavelet bases are stable in the Sobolev spaces Hs for jsj jsj on Lipschitz manifolds and the wavelets can in principal be arranged to have any desired order of vanishing moments As a consequence these bases can be used ...

A multiplicative Schwarz overlapping domain decomposition method is considered for solving elliptic boundary value problems. By equipping the relevant Sobolev spaces on the subdomains with wavelet bases, adaptive wavelet methods are used for approximately solving the subdomain problems. The union of the wavelet bases forms a frame for the Sobolev space on the domain as a whole. The resulting me...

Adaptive mesh refinement techniques are nowadays an established and powerful tool for the numerical discretization of PDE’s. In recent years, wavelet bases have been proposed as an alternative to these techniques. The main motivation for the use of such bases in this context is their good performances in data compression and the approximation theoretic foundations which allow to analyze and opt...