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Permanent link (DOI): https://doi.org/10.7939/R32Z1338Z

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A Systematic Construction of Multiwavelets on the Unit Interval Open Access

Descriptions

Other title
Subject/Keyword
Riesz wavelets
Numerical differential equations
Sobolev spaces
Multiwavelets
Bounded interval
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Michelle, Michelle
Supervisor and department
Han, Bin (Mathematical and Statistical Sciences)
Examining committee member and department
Dai, Feng (Mathematical and Statistical Sciences)
Wong, Yau Shu (Mathematical and Statistical Sciences)
Han, Bin (Mathematical and Statistical Sciences)
Minev, Peter (Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Applied Mathematics
Date accepted
2017-08-21T14:57:28Z
Graduation date
2017-11:Fall 2017
Degree
Master of Science
Degree level
Master's
Abstract
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.
Language
English
DOI
doi:10.7939/R32Z1338Z
Rights
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. 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.
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