Restricted nonlinear approximation and singular solutions of boundary integral equations
Publikation: Beiträge in Zeitschriften › Zeitschriftenaufsätze › Forschung › begutachtet
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Restricted nonlinear approximation and singular solutions of boundary integral equations. / Hochmuth, Reinhard.
in: Approximation Theory and Its Applications, Jahrgang 18, Nr. 1, 2002, S. 1-25.Publikation: Beiträge in Zeitschriften › Zeitschriftenaufsätze › Forschung › begutachtet
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TY - JOUR
T1 - Restricted nonlinear approximation and singular solutions of boundary integral equations
AU - Hochmuth, Reinhard
PY - 2002
Y1 - 2002
N2 - This paper studies several problems, which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterizations of functions in Besov spaces B 6r,r (0.1) with 0<σ<∞ and (1+σ)−1<r<∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results.
AB - This paper studies several problems, which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterizations of functions in Besov spaces B 6r,r (0.1) with 0<σ<∞ and (1+σ)−1<r<∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results.
KW - Mathematics
U2 - 10.1007/BF02837045
DO - 10.1007/BF02837045
M3 - Journal articles
VL - 18
SP - 1
EP - 25
JO - Approximation Theory and Its Applications
JF - Approximation Theory and Its Applications
SN - 1000-9221
IS - 1
ER -