Rotationally Invariant Quadratures for the Sphere

  title={Rotationally Invariant Quadratures for the Sphere},
  author={Cory Ahrens and Gregory Beylkin},
We construct near-optimal quadratures for the sphere that are invariant under the icosahedral rotation group. These quadratures integrate all (N + 1)2 linearly independent functions in a rotationally invariant subspace of maximal order and degree N . The nodes of these quadratures are nearly uniformly distributed, and the number of nodes is only marginally more than the optimal (N + 1)2/3 nodes. Using these quadratures, we discretize the reproducing kernel on a rotationally invariant subspace… CONTINUE READING
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