Full metadata
Title
Efficient and Well-Conditioned Methods for Computing Frame Approximations
Description
This thesis addresses the problem of approximating analytic functions over general and compact multidimensional domains. Although the methods we explore can be used in complex domains, most of the tests are performed on the interval $[-1,1]$ and the square $[-1,1]\times[-1,1]$. Using Fourier and polynomial frame approximations on an extended domain, well-conditioned methods can be formulated. In particular, these methods provide exponential decay of the error down to a finite but user-controlled tolerance $\epsilon>0$. Additionally, this thesis explores two implementations of the frame approximation: a singular value decomposition (SVD)-regularized least-squares fit as described by Adcock and Shadrin in 2022, and a column and row selection method that leverages QR factorizations to reduce the data needed in the approximation. Moreover, strategies to reduce the complexity of the approximation problem by exploiting randomized linear algebra in low-rank algorithms are also explored, including the AZ algorithm described by Coppe and Huybrechs in 2020.
Date Created
2023
Contributors
- Guo, Maosheng (Author)
- Platte, Rodrigo (Thesis advisor)
- Espanol, Malena (Committee member)
- Renaut, Rosemary (Committee member)
- Arizona State University (Publisher)
Topical Subject
Resource Type
Extent
45 pages
Language
eng
Copyright Statement
In Copyright
Primary Member of
Peer-reviewed
No
Open Access
No
Handle
https://hdl.handle.net/2286/R.2.N.187776
Level of coding
minimal
Cataloging Standards
Note
Partial requirement for: M.A., Arizona State University, 2023
Field of study: Applied Mathematics
System Created
- 2023-06-07 12:27:33
System Modified
- 2023-06-07 12:27:39
- 1 year 5 months ago
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