Adaptive Wavelet Methods
Karsten Urban · Oxford University Press eBooks · 2008
This chapter starts by adaptively approximating a given function and introduce the main theoretical concepts. After describing the more classical approach to adaptivity based upon a-posteriori error estimates, it shows the somewhat different perspective of adaptive wavelet methods. Given an operator equation, an equivalent infinite-dimensional problem on sequence spaces is introduced. In order to obtain a computable method, the infinite operator is replaced by an approximate application. The resulting schemes are described, analyzed and compared by numerical experiments. An outlook to nonlinear operators is given.