Full metadata
Title
Optimal sampling for linear function approximation and high-order finite difference methods over complex regions
Description
I focus on algorithms that generate good sampling points for function approximation. In 1D, it is well known that polynomial interpolation using equispaced points is unstable. On the other hand, using Chebyshev nodes provides both stable and highly accurate points for polynomial interpolation. In higher dimensional complex regions, optimal sampling points are not known explicitly. This work presents robust algorithms that find good sampling points in complex regions for polynomial interpolation, least-squares, and radial basis function (RBF) methods. The quality of these nodes is measured using the Lebesgue constant. I will also consider optimal sampling for constrained optimization, used to solve PDEs, where boundary conditions must be imposed. Furthermore, I extend the scope of the problem to include finding near-optimal sampling points for high-order finite difference methods. These high-order finite difference methods can be implemented using either piecewise polynomials or RBFs.
Date Created
2019
Contributors
- Liu, Tony (Author)
- Platte, Rodrigo B (Thesis advisor)
- Renaut, Rosemary (Committee member)
- Kaspar, David (Committee member)
- Moustaoui, Mohamed (Committee member)
- Motsch, Sebastien (Committee member)
- Arizona State University (Publisher)
Topical Subject
Resource Type
Extent
viii, 89 pages : illustrations (some color)
Language
eng
Copyright Statement
In Copyright
Primary Member of
Peer-reviewed
No
Open Access
No
Handle
https://hdl.handle.net/2286/R.I.54897
Statement of Responsibility
by Tony Liu
Description Source
Viewed on September 10, 2020
Level of coding
full
Note
thesis
Partial requirement for: Ph.D., Arizona State University, 2019
bibliography
Includes bibliographical references (pages 86-89)
Field of study: Mathematics
System Created
- 2019-11-06 03:39:08
System Modified
- 2021-08-26 09:47:01
- 3 years 2 months ago
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