Hyperinterpolations on the Sphere

  • Author / Creator
  • 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

  • Subjects / Keywords
  • Graduation date
    Fall 2014
  • Type of Item
  • Degree
    Master of Science
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.