Handling Wavelet Expansions in numerical Methods

Arend Aalberthus Roeland Metselaar

Research output: ThesisPhD Thesis - Research UT, graduation UTAcademic

Abstract

Wavelet expansions have drawn a lot of attention in recent decades. Wavelets originate from signal analysis, and one of the purposes is data compression. The ability to compress data can also be used to reduce the amount of computation work in a numerical simulation.A family of wavelets forms a basis for a function space. Most adaptive wavelet methods are based on expansions of functions in a freely selectable subset of such a basis. This avoids the often expensive, grid generation step needed in most other adaptive methods, but leads to more complicated bookkeeping.A large part of this thesis is devoted to the problem of performing this bookkeeping efficiently. Some methods divide the wavelet expansion into parts of decreasing importance. Using an approximate division is often more efficient than using the best division, which requires all terms in the expansion to be sorted.
LanguageUndefined
Supervisors/Advisors
  • Traas, C.R., Supervisor
  • van Damme, Rudolf Martinus Josephus, Advisor
Award date20 Jun 2002
Place of PublicationEnschede
Publisher
Print ISBNs90-36-51771-0
Publication statusPublished - 20 Jun 2002

Keywords

  • IR-38630
  • METIS-206125

Cite this

Metselaar, A. A. R. (2002). Handling Wavelet Expansions in numerical Methods. Enschede: Twente University Press (TUP).
Metselaar, Arend Aalberthus Roeland. / Handling Wavelet Expansions in numerical Methods. Enschede : Twente University Press (TUP), 2002. 119 p.
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author = "Metselaar, {Arend Aalberthus Roeland}",
year = "2002",
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Metselaar, AAR 2002, 'Handling Wavelet Expansions in numerical Methods', Enschede.

Handling Wavelet Expansions in numerical Methods. / Metselaar, Arend Aalberthus Roeland.

Enschede : Twente University Press (TUP), 2002. 119 p.

Research output: ThesisPhD Thesis - Research UT, graduation UTAcademic

TY - THES

T1 - Handling Wavelet Expansions in numerical Methods

AU - Metselaar, Arend Aalberthus Roeland

PY - 2002/6/20

Y1 - 2002/6/20

N2 - Wavelet expansions have drawn a lot of attention in recent decades. Wavelets originate from signal analysis, and one of the purposes is data compression. The ability to compress data can also be used to reduce the amount of computation work in a numerical simulation.A family of wavelets forms a basis for a function space. Most adaptive wavelet methods are based on expansions of functions in a freely selectable subset of such a basis. This avoids the often expensive, grid generation step needed in most other adaptive methods, but leads to more complicated bookkeeping.A large part of this thesis is devoted to the problem of performing this bookkeeping efficiently. Some methods divide the wavelet expansion into parts of decreasing importance. Using an approximate division is often more efficient than using the best division, which requires all terms in the expansion to be sorted.

AB - Wavelet expansions have drawn a lot of attention in recent decades. Wavelets originate from signal analysis, and one of the purposes is data compression. The ability to compress data can also be used to reduce the amount of computation work in a numerical simulation.A family of wavelets forms a basis for a function space. Most adaptive wavelet methods are based on expansions of functions in a freely selectable subset of such a basis. This avoids the often expensive, grid generation step needed in most other adaptive methods, but leads to more complicated bookkeeping.A large part of this thesis is devoted to the problem of performing this bookkeeping efficiently. Some methods divide the wavelet expansion into parts of decreasing importance. Using an approximate division is often more efficient than using the best division, which requires all terms in the expansion to be sorted.

KW - IR-38630

KW - METIS-206125

M3 - PhD Thesis - Research UT, graduation UT

SN - 90-36-51771-0

PB - Twente University Press (TUP)

CY - Enschede

ER -

Metselaar AAR. Handling Wavelet Expansions in numerical Methods. Enschede: Twente University Press (TUP), 2002. 119 p.