Localized Linear Polynomial Operators and Quadrature Formulas on the Sphere
نویسندگان
چکیده
منابع مشابه
Localized Linear Polynomial Operators and Quadrature Formulas on the Sphere
The purpose of this paper is to construct universal, auto-adaptive, localized, linear, polynomial (-valued) operators based on scattered data on the (hyper) sphere Sq (q ≥ 2). The approximation and localization properties of our operators are studied theoretically in deterministic as well as probabilistic settings. Numerical experiments are presented to demonstrate their superiority over tradit...
متن کاملLocalized Linear Polynomial Operators on the Sphere
The purpose of this paper is to construct universal, auto–adaptive, localized, linear, polynomial (-valued) operators based on scattered data on the (hyper–)sphere Sq (q ≥ 2). The approximation and localization properties of our operators are studied theoretically in deterministic as well as probabilistic settings. Numerical experiments are presented to demonstrate their superiority over tradit...
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Let q ≥ 1 be an integer, Sq be the unit sphere embedded in Rq+1, and μq be the volume element of Sq. For x0 ∈ Sq, and α ∈ (0, π), let Sα(x0) denote the cap {ξ ∈ Sq : x0 · ξ ≥ cosα}. We prove that for any integer m ≥ 1, there exists a positive constant c = c(q,m), independent of α, with the following property. Given an arbitrary set C of points in Sα(x0), satisftying the mesh norm condition max ...
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15 صفحه اولSeveral New Quadrature Formulas for Polynomial Integration in the Triangle
We present several new quadrature formulas in the triangle for exact integrationof polynomials. The points were computed numerically with a cardinal function algorithm whichimposes that the number of quadrature points N be equal to the dimension of a lower dimensionalpolynomial space. Quadrature forumulas are presented for up to degree d = 25, all which havepositive weights and ...
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2009
ISSN: 0036-1429,1095-7170
DOI: 10.1137/060678555