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Optimal Sampling for Linear Function Approximation and High-Order Finite Difference Methods over Complex Regions


Abstract 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 imp... (more)
Created Date 2019
Contributor Liu, Tony (Author) / Platte, Rodrigo B (Advisor) / Renaut, Rosemary (Committee member) / Kaspar, David (Committee member) / Moustaoui, Mohamed (Committee member) / Motsch, Sebastien (Committee member) / Arizona State University (Publisher)
Subject Applied mathematics / Finite Difference Methods / Function Approximation / Lebesgue Constant / Optimal Sampling
Type Doctoral Dissertation
Extent 98 pages
Language English
Copyright
Note Doctoral Dissertation Mathematics 2019
Collaborating Institutions Graduate College / ASU Library
Additional Formats MODS / OAI Dublin Core / RIS


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Description Dissertation/Thesis