Title: Compactly supported Powell-Sabin spline multiwavelets in Sobolev spaces
Authors: Maes, Jan ×
Bultheel, Adhemar
Issue Date: May-2005
Publisher: Department of Computer Science, K.U.Leuven
Series Title: TW Reports vol:TW428
Abstract: In this paper we construct Powell--Sabin spline multiwavelets on the hexagonal lattice in a shift-invariant setting. This allows us to use Fourier techniques to study the range of the smoothness parameter s for which the wavelet basis is a Riesz basis in the Sobolev space Hs(R²) and we find that 0.360704 < s < 5/2. For those s, discretizations of Hs-elliptic problems with respect to the wavelet basis lead to uniformly well-conditioned stiffness matrices, resulting in an asymptotically optimal preconditioning method.
Publication status: published
KU Leuven publication type: IR
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author

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