Spherical configurations and quadrature methods for integral equations of the second kind
In this paper, we propose and analyze a product integration method for the second-kind
integral equation with weakly singular and continuous kernels on the unit sphere $\mathbb …
integral equation with weakly singular and continuous kernels on the unit sphere $\mathbb …
The algebra of hyperinterpolation-class on the sphere
C An, J Ran - arXiv preprint arXiv:2404.00523, 2024 - arxiv.org
This paper considers the so-called concept of hyperinterpolation-class, ie, the set of all
operators derived from the hyperinterpolation operator on the unit sphere. Concretely, we …
operators derived from the hyperinterpolation operator on the unit sphere. Concretely, we …
Numerical integration over the unit sphere by using spherical t-design
C An, S Chen - arXiv preprint arXiv:1611.02785, 2016 - arxiv.org
This paper studies numerical integration over the unit sphere $\mathbb {S}^
2\subset\mathbb {R}^{3} $ by using spherical $ t $-design, which is an equal positive …
2\subset\mathbb {R}^{3} $ by using spherical $ t $-design, which is an equal positive …
Numerical construction of spherical t-designs by Barzilai-Borwein method
Abstract A point set XN on the unit sphere is a spherical t-design is equivalent to the
nonnegative quantity AN, t+ 1 vanished. We show that if XN is a stationary point set of AN, t+ …
nonnegative quantity AN, t+ 1 vanished. We show that if XN is a stationary point set of AN, t+ …
Quadrature rules with neighborhood of spherical designs on the two-sphere
Y Zhou - Applied Mathematics and Computation, 2020 - Elsevier
In this paper, we concentrate on quadrature rules with their point sets located on a
neighborhood of a spherical design. We show that any point set in a small enough …
neighborhood of a spherical design. We show that any point set in a small enough …