236 | IGPM236.pdf October 2003 |
TITLE | Adaptive Application of Operators in Standard Representation |
AUTHORS | Arne Barinka, Stephan Dahlke, Wolfgang Dahmen |
ABSTRACT | Recently adaptive wavelet methods have been developed which can be shown to exhibit an asymptotically optimal accuracy/work balance for a wide class of variational problems including classical elliptic boundary value problems, boundary integral equations as well as certain classes of non coercive problems such as saddle point problems [8, 9, 12]. A core ingredient of these schemes is the approximate application of the involved operators in standard wavelet representation. Optimal computational complexity could be shown under the assumption that the entries in properly compressed standard representations are known or computable in average at unit cost. In this paper we propose concrete computational strategies and show under which circumstances this assumption is justified in the context of elliptic boundary value problems. |
KEYWORDS | operator equations, quasi sparse matrices and vectors, best N-term approximation, fast matrix/vector multiplication |
DOI | 10.1007/s10444-004-7631-2 |
PUBLICATION | Advances in computational mathematics : AICM 24, 5-34 (2006) |