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.
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- Partial requirement for: Ph.D., Arizona State University, 2019Note typethesis
- Includes bibliographical references (pages 86-89)Note typebibliography
- Field of study: Mathematics