Spherical designs

1979 ◽  
pp. 255-272 ◽  
Author(s):  
J.-M. Goethals ◽  
J. J. Seidel
Keyword(s):  
Spherical Designs

scholarly journals Improve concentration of frequency and time (ConceFT) by novel complex spherical designs

2021 ◽  
Vol 54 ◽  
pp. 137-144
Author(s):  
Matt Sourisseau ◽  
Yu Guang Wang ◽  
Robert S. Womersley ◽  
Hau-Tieng Wu ◽  
Wei-Hsuan Yu
Keyword(s):  
Spherical Designs ◽  
Novel Complex

scholarly journals Spectral Limitations of Quadrature Rules and Generalized Spherical Designs

2019 ◽  
Author(s):  
Stefan Steinerberger
Keyword(s):  
Quadrature Rule ◽  
Quadrature Rules ◽  
Dimensional Manifold ◽  
Spherical Designs

Abstract We study manifolds $M$ equipped with a quadrature rule \begin{equation*} \int_{M}{\phi(x)\,\mathrm{d}x} \simeq \sum_{i=1}^{n}{a_i \phi(x_i)}.\end{equation*}We show that $n$-point quadrature rules with nonnegative weights on a compact $d$-dimensional manifold cannot integrate more than at most the 1st $c_{d}n + o(n)$ Laplacian eigenfunctions exactly. The constants $c_d$ are explicitly computed and $c_2 = 4$. The result is new even on $\mathbb{S}^2$ where it generalizes results on spherical designs.

Regularized Least Squares Approximations on the Sphere Using Spherical Designs

2012 ◽  
Vol 50 (3) ◽  
pp. 1513-1534 ◽  
Author(s):  
Congpei An ◽  
Xiaojun Chen ◽  
Ian H. Sloan ◽  
Robert S. Womersley
Keyword(s):  
Least Squares ◽  
Spherical Designs ◽  
Regularized Least Squares

Polynomial techniques for investigation of spherical designs

2008 ◽  
Vol 51 (3) ◽  
pp. 275-288 ◽  
Author(s):  
Silvia Boumova ◽  
Peter Boyvalenkov ◽  
Hristina Kulina ◽  
Maya Stoyanova
Keyword(s):  
Spherical Designs

scholarly journals Spherical Designs via Brouwer Fixed Point Theorem

2010 ◽  
Vol 24 (1) ◽  
pp. 207-217 ◽  
Author(s):  
Andriy V. Bondarenko ◽  
Maryna S. Viazovska
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Spherical Designs ◽  
Brouwer Fixed Point Theorem
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