Cubature Formulas on Spheres

  • Feng Dai
  • Yuan Xu
Part of the Springer Monographs in Mathematics book series (SMM)


In problems that deal with data, as frequently encountered in applied mathematics, it is often necessary to discretize integrals to obtain discrete processes of approximation. Cubature formulas, a synonym for numerical integration formulas, are essential tools for discretizing integrals. In contrast to the one-variable case, fundamental problems of cubature formulas in several variables are still open, including those on the sphere. In this chapter, we discuss several aspects of cubature formulas on the sphere.


Quadrature Formula Quadrature Rule Cubature Formula Harmonic Polynomial Asymptotic Order 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Feng Dai
    • 1
  • Yuan Xu
    • 2
  1. 1.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada
  2. 2.Department of MathematicsUniversity of OregonEugeneUSA

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