Name
Abstract | ||
|---|---|---|
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 Sαq(x0) denote the cap {ξ ∈ Sq : x0 ċ ξ ≥ cos α}. 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 Sαq(x0), satisfying the mesh norm condition maxξ∈Sαq(x0) minζ∈C dist(ξ,ζ) ≤ cα, there exist nonnegative weights wξ, ξ ∈ C, such that ∫Sαq(x0) P(ζ)dµq(ζ) = Σξ ∈C wξP(ξ) for every spherical polynomial P of degree at most m. Similar quadrature formulas are also proved for spherical bands. |
Year | DOI | Venue |
|---|---|---|
2004 | 10.1016/j.jco.2003.06.005 | J. Complexity |
Keywords | DocType | Volume |
nonnegative weights w,local quadrature formula,C dist,mesh norm condition max,following property,C w,spherical band,spherical polynomial P,positive constant c,arbitrary set,integer m | Journal | 20 |
Issue | ISSN | Citations |
5 | Journal of Complexity | 5 |
PageRank | References | Authors |
0.66 | 11 | 1 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hrushikesh Narhar Mhaskar | 1 | 257 | 61.07 |