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Permanent link (DOI): https://doi.org/10.7939/R3445HM52

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Hyperinterpolations on the Sphere Open Access

Descriptions

Other title
Subject/Keyword
Approximation order
Cubature formula
Hyperinterpolation
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Chu,xingming
Supervisor and department
Han,Bin(Department of mathematical and statistical sciences)
Dai,Feng(Department of mathematical and statistical sciences)
Examining committee member and department
Dai, Feng(Department of mathematical and statistical sciences)
Zhang, Tong(Department of mathematical and statistical sciences)
Han, Bin(Department of mathematical and statistical sciences)
Yu, xinwei((Department of mathematical and statistical sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematics
Date accepted
2014-04-23T13:54:21Z
Graduation date
2014-11
Degree
Master of Science
Degree level
Master's
Abstract
Hyperinterpolation on the unit sphere of the Euclidean space was proposed by Sloan in 1995. But pointwise convergence in the uniform form can not be achieved by hyperinterpolation. Reimer later proposed the generalized hyperinterpolation, which has the advantages that uniform convergence for all continuous functions can be achieved and it requires positive cubature formulas of less precision and hence significantly reduces the cost of computations. However, Reimers technique only allows him to obtain best approximation order result for C1 functions. The main purpose of this thesis is to consider generalized hyperinterpolation of higher order and a best approximation order is obtained. The smoothness of functions is measured in terms of a new K-functional we introduced. Finally, the thesis also collects several useful positive cubature formulas and discusses briefly the construction methods.
Language
English
DOI
doi:10.7939/R3445HM52
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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