Name
Abstract | ||
|---|---|---|
A well-known method of estimating the length of a parametric curve in Rd is to sample some points from it and compute the length of the polygon passing through them. In this paper we show that for uniform sampling of regular smooth curves, Richardson extrapolation can be applied repeatedly giving a sequence of derivative-free length estimates of arbitrarily high orders of accuracy. A similar result is derived for the approximation of the area of parametric surfaces. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1007/s11075-007-9095-1 | Numerical Algorithms |
Keywords | Field | DocType |
Richardson extrapolation,Arc length,Surface area,Primary 65D30,65B05,Secondary 41A58,65D17 | Parametric surface,Mathematical optimization,Parametric equation,Polygon,Richardson extrapolation,Smooth curves,Mathematical analysis,Arc length,Extrapolation,Sampling (statistics),Mathematics | Journal |
Volume | Issue | ISSN |
44 | 3 | 1017-1398 |
Citations | PageRank | References |
0 | 0.34 | 8 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michael S. Floater | 1 | 1333 | 117.22 |
| Atgeirr F. Rasmussen | 2 | 0 | 0.34 |
| Ulrich Reif | 3 | 0 | 0.34 |