Note on 1D quarklet approximation
Note on 1D quarklet approximation
Dokument öffnen (114KB)Datum der Veröffentlichung
03.2020Verlag / herausgebende Einrichtung
Institut für Numerische Simulation (INS)Verlagsort
BonnMetadaten
Zur Langanzeige
Zitierbarer Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11797
Inhalt
On the example of the simplest C0 spline quarklet construction of [1], we demonstrate the possible reduction of the complexity estimates for the approximation of singularity functions on the unit interval given in [3], to come closer to the complexity estimates known for hp-methods. To come up with a simplified argument, we explore the fact that the CDF biorthogonal spline wavelets [2] used in the construction of quarklets can be obtained by the lifting scheme [4]. Similar results are also possible for spline quarklet systems built from smooth B-splines with higher order of vanishing moments.
Schlagwörter
Quarklets, subexponential rates, hp-approximation
Klassifikation (DDC)
510 Mathematik 518 Numerische AnalysisErstpublikation
https://ins.uni-bonn.de/publication/preprintsReihe, Nummer
INS Preprints ; 2003Peter Oswald: Note on 1D quarklet approximation. In: INS Preprints, 2003.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11797
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11797
@unpublished{handle:20.500.11811/11797,
author = {{ }},
title = {Note on 1D quarklet approximation},
publisher = {Institut für Numerische Simulation (INS)},
year = 2020,
month = mar,
INS Preprints},
volume = 2003,
note = {On the example of the simplest C0 spline quarklet construction of [1], we demonstrate the possible reduction of the complexity estimates for the approximation of singularity functions on the unit interval given in [3], to come closer to the complexity estimates known for hp-methods. To come up with a simplified argument, we explore the fact that the CDF biorthogonal spline wavelets [2] used in the construction of quarklets can be obtained by the lifting scheme [4]. Similar results are also possible for spline quarklet systems built from smooth B-splines with higher order of vanishing moments.},
url = {https://hdl.handle.net/20.500.11811/11797}
}
author = {{ }},
title = {Note on 1D quarklet approximation},
publisher = {Institut für Numerische Simulation (INS)},
year = 2020,
month = mar,
INS Preprints},
volume = 2003,
note = {On the example of the simplest C0 spline quarklet construction of [1], we demonstrate the possible reduction of the complexity estimates for the approximation of singularity functions on the unit interval given in [3], to come closer to the complexity estimates known for hp-methods. To come up with a simplified argument, we explore the fact that the CDF biorthogonal spline wavelets [2] used in the construction of quarklets can be obtained by the lifting scheme [4]. Similar results are also possible for spline quarklet systems built from smooth B-splines with higher order of vanishing moments.},
url = {https://hdl.handle.net/20.500.11811/11797}
}
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