Handling Wavelet Expansions in numerical Methods

Arend Aalberthus Roeland Metselaar

    Research output: ThesisPhD Thesis - Research UT, graduation UT

    66 Downloads (Pure)

    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.
    Original 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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    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 UT

    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.