Name
Abstract | ||
|---|---|---|
Geodetic and meteorological data, collected via satellites for ex- ample, are genuinely scattered, and not confined to any special set of points. Even so, known quadrature formulas used in numerically computing integrals involving such data have had restrictions either on the sites (points) used or, more significantly, on the number of sites required. Here, for the unit sphere embedded in Rq, we obtain quadrature formulas that are exact for spherical harmonics of a fixed order, have nonnegative weights, and are based on function values at scattered sites. To be exact, these formulas require only a number of sites comparable to the dimension of the space. As a part of the proof, we derive L1-Marcinkiewicz-Zygmund inequalities for such sites.1 |
Year | DOI | Venue |
|---|---|---|
2001 | 10.1090/S0025-5718-00-01240-0 | Math. Comput. |
Keywords | Field | DocType |
scattered-data on spheres.,spherical marcinkiewicz-zygmund inequality,. marcinkiewicz-zygmund inequalities,quadrature,positive quadrature,data collection,spherical harmonic | Gauss–Kronrod quadrature formula,Harmonic function,Eigenfunction,Mathematical analysis,Numerical integration,Legendre polynomials,Spherical harmonics,Quadrature (mathematics),Mathematics,Unit sphere | Journal |
Volume | Issue | ISSN |
70 | 235 | 0025-5718 |
Citations | PageRank | References |
46 | 12.69 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hrushikesh Narhar Mhaskar | 1 | 257 | 61.07 |
| F. J. Narcowich | 2 | 89 | 19.20 |
| J. D. Ward | 3 | 46 | 12.69 |