caa a22 4500 467939160 CHVBK 20180406153007.0 cr unu---uuuuu 170328e20060101xx s 000 0 eng 10.1007/s10444-004-7631-2 doi (NATIONALLICENCE)springer-10.1007/s10444-004-7631-2 Adaptive application of operators in standard representation [Elektronische Daten] [Arne Barinka, Stephan Dahlke, Wolfgang Dahmen] 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 noncoercive problems such as saddle point problems. 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. Springer, 2006 operator equations nationallicence quasi-sparse matrices and vectors nationallicence best N -term approximation nationallicence fast matrix/vector multiplication nationallicence Barinka Arne Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, 52056, Aachen, Germany aut Dahlke Stephan Philipps-Universität Marburg, FB12 Mathematik und Informatik, Hans-Meerwein Straße, Lahnberge, 35032, Marburg, Germany aut Dahmen Wolfgang Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, 52056, Aachen, Germany aut Advances in Computational Mathematics Kluwer Academic Publishers 24/1-4(2006-01-01), 5-34 1019-7168 24:1-4<5 2006 24 10444 https://doi.org/10.1007/s10444-004-7631-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10444-004-7631-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Barinka Arne Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, 52056, Aachen, Germany aut NATIONALLICENCE 700 1- Dahlke Stephan Philipps-Universität Marburg, FB12 Mathematik und Informatik, Hans-Meerwein Straße, Lahnberge, 35032, Marburg, Germany aut NATIONALLICENCE 700 1- Dahmen Wolfgang Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, 52056, Aachen, Germany aut NATIONALLICENCE 773 0- Advances in Computational Mathematics Kluwer Academic Publishers 24/1-4(2006-01-01), 5-34 1019-7168 24:1-4<5 2006 24 10444 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer