Well Conditioned Spherical Designs for Integration and Interpolation on the Two-Sphere

  title={Well Conditioned Spherical Designs for Integration and Interpolation on the Two-Sphere},
  author={Congpei An and Xiaojun Chen and Ian H. Sloan and Robert S. Womersley},
  journal={SIAM J. Numer. Anal.},
A set $\mathcal{X}_{N}$ of $N$ points on the unit sphere is a spherical $t$-design if the average value of any polynomial of degree at most $t$ over $\mathcal{X}_{N}$ is equal to the average value of the polynomial over the sphere. This paper considers the characterization and computation of spherical $t$-designs on the unit sphere $\mathbb{S}^2\subset\mathbb{R}^3$ when $N\geq(t+1)^2$, the dimension of the space $\mathbb{P}_t$ of spherical polynomials of degree at most $t$. We show how to… 

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