NAMColloquium Samplets: Construction and scattered data compression |  |
Speaker:Prof. Dr. Michael Multerer, Università della Svizzera italiana, Lugano, Switzerland
Organizer:Institut für Numerische und Angewandte Mathematik
Details:
We introduce the concept of samplets by transferring the construction
of Tausch-White wavelets to scattered data. The result is a
multiresolution analysis tailored to discrete data sets. This directly
enables compression, feature detection, and adaptivity. The cost for
constructing a samplet basis and the fast samplet transform, respectively,
is linear in the size of the underlying data set.
We employ samplets with vanishing moments to compress kernel
matrices for efficient scattered data approximation. In particular,
one can prove that the compressed matrices are essentially sparse,
while the entailed approximation error is controllable by the number
of vanishing moments. We finish the presentation with numerical studies
for scattered data approximation with sparsity constraints.
of Tausch-White wavelets to scattered data. The result is a
multiresolution analysis tailored to discrete data sets. This directly
enables compression, feature detection, and adaptivity. The cost for
constructing a samplet basis and the fast samplet transform, respectively,
is linear in the size of the underlying data set.
We employ samplets with vanishing moments to compress kernel
matrices for efficient scattered data approximation. In particular,
one can prove that the compressed matrices are essentially sparse,
while the entailed approximation error is controllable by the number
of vanishing moments. We finish the presentation with numerical studies
for scattered data approximation with sparsity constraints.
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Type:Colloquium
Language:English
Category:Research
Host:Prof. Dr. Gerlind Plonka-Hoch
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Direct link to event:https://events.goettingen-campus.de/event?eventId=10216949
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