Hyperinterpolations on the Sphere

• Author / Creator

  Chu,xingming

• 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.

• Subjects / Keywords

  • Approximation order
  • Cubature formula
  • Hyperinterpolation

• Graduation date

  Fall 2014

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R3445HM52

• 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.