For certain classes of operator equations, adaptive wavelet methods have recently been proven
to converge with optimal rates, i.e., with the same relation between the achieved accuracy
and the associated computational work that is observable for best nonlinear approximations.
In order to verify these theoretical results by suitable computer code,
the convergence analysis has to be complemented by a judicious software design.
This talk provides details on the implementation of adaptive wavelet and
wavelet frame methods, in particular concerning data structures and algorithms that
preserve optimal computational complexity.
As a reference implementation, I will focus on the C++ software library
which is currently used by the group of S. Dahlke and collaborators.
Numerical examples are given from the adaptive wavelet
discretization of elliptic and parabolic boundary value problems,
as well as associated inverse problems.