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

  • Multiwavelets
  • Sobolev spaces
  • Numerical differential equations
  • Bounded interval
  • Riesz wavelets

• Graduation date

  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.