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We present a novel Galerkin method for solving partial differential equations on the sphere. The problem is discretized by a highly localized basis which is easily constructed. The stiffness matrix entries are computed by a recently developed quadrat
Externí odkaz:
http://arxiv.org/abs/1404.5263
Quadrature formulas for spheres, the rotation group, and other compact, homogeneous manifolds are important in a number of applications and have been the subject of recent research. The main purpose of this paper is to study coordinate independent qu
Externí odkaz:
http://arxiv.org/abs/1211.5171
Publikováno v:
SIAM J. Numer. Anal. 51-5 (2013), pp. 2538-2562
Approximation/interpolation from spaces of positive definite or conditionally positive definite kernels is an increasingly popular tool for the analysis and synthesis of scattered data, and is central to many meshless methods. For a set of $N$ scatte
Externí odkaz:
http://arxiv.org/abs/1205.3255
In this article we investigate the feasibility of constructing stable, local bases for computing with kernels. In particular, we are interested in constructing families $(b_{\xi})_{\xi\in\Xi}$ that function as bases for kernel spaces $S(k,\Xi)$ so th
Externí odkaz:
http://arxiv.org/abs/1111.1013
Publikováno v:
Foundations of Computational Mathematics. October 2012, Volume 12, Issue 5, pp 625-670
This article is devoted to developing a theory for effective kernel interpolation and approximation in a general setting. For a wide class of compact, connected $C^\infty$ Riemannian manifolds, including the important cases of spheres and SO(3), we e
Externí odkaz:
http://arxiv.org/abs/1012.4852
Publikováno v:
Journal of Fourier Analysis and Applications: Volume 18, Issue 1 (2012), Page 67-86
In this paper, interpolation by scaled multi-integer translates of Gaussian kernels is studied. The main result establishes $L_p$ Sobolev error estimates and shows that the error is controlled by the $L_p$ multiplier norm of a Fourier multiplier clos
Externí odkaz:
http://arxiv.org/abs/1008.3168
The purpose of this paper is to establish L^p error estimates, a Bernstein inequality, and inverse theorems for approximation by a space comprising spherical basis functions located at scattered sites on the unit n-sphere. In particular, the Bernstei
Externí odkaz:
http://arxiv.org/abs/0810.5075
Publikováno v:
Mathematics of Computation, 2018 Sep 01. 87(313), 2233-2258.
Externí odkaz:
https://www.jstor.org/stable/90021984
Publikováno v:
Mathematics of Computation, 2018 Jul 01. 87(312), 1949-1989.
Externí odkaz:
https://www.jstor.org/stable/90021441