Multiscale analysis in Sobolev spaces on bounded domains |
| |
Authors: | Holger Wendland |
| |
Institution: | 1. Mathematical Institute, University of Oxford, 24–29 St Giles’, Oxford, OX1 3LB, England
|
| |
Abstract: | We study a multiscale scheme for the approximation of Sobolev functions on bounded domains. Our method employs scattered data
sites and compactly supported radial basis functions of varying support radii at scattered data sites. The actual multiscale
approximation is constructed by a sequence of residual corrections, where different support radii are employed to accommodate
different scales. Convergence theorems for the scheme are proven, and it is shown that the condition numbers of the linear
systems at each level are independent of the level, thereby establishing for the first time a mathematical theory for multiscale
approximation with scaled versions of a single compactly supported radial basis function at scattered data points on a bounded
domain. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|