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A Systematic Construction of Multiwavelets on the Unit Interval

  • Author / Creator
    Michelle, Michelle
  • One main goal of this thesis is to bring forth a systematic and simple construction of a multiwavelet basis on a bounded interval. The construction that we present possesses orthogonality in the derivatives of the multiwavelet basis among all scale levels. Since we are mainly interested in Riesz wavelets, we call such wavelets mth derivative--orthogonal Riesz wavelets. Furthermore, we present some necessary and sufficient conditions as to when such a construction can be done. We show that our constructed multiwavelet bases possess many desirable properties such as symmetry, stability, and short support. The second goal of this thesis is to provide some conditions that guarantee a Riesz wavelet in L_{2}(R) can be adapted so that it forms a Riesz wavelet for L_{2}(I), where I is a bounded interval. As the third goal of this thesis, we also evaluate the performance of the newly constructed bases in obtaining the numerical solutions to some differential equations to showcase their potential usefulness. More specifically, we show how the resulting coefficient matrices are sparse and have a low condition number.

  • Subjects / Keywords
  • Graduation date
    2017-11:Fall 2017
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R32Z1338Z
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Applied Mathematics
  • Supervisor / co-supervisor and their department(s)
    • Han, Bin (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Minev, Peter (Mathematical and Statistical Sciences)
    • Han, Bin (Mathematical and Statistical Sciences)
    • Dai, Feng (Mathematical and Statistical Sciences)
    • Wong, Yau Shu (Mathematical and Statistical Sciences)