Name
Abstract | ||
|---|---|---|
The paper develops a necessary condition for the regularity of a multivariate re- finable function in terms of a factorization property of the associated subdivision mask. The extension to arbitrary isotropic dilation matrices necessitates the introduction of the concepts of restricted and renormalized convergence of a subdivision scheme as well as the notion of subconvergence, i.e., the convergence of only a subsequence of the iterations of the subdivi- sion scheme. Since, in addition, factorization methods pass even from scalar to matrix valued refinable functions, those results have to be formulated in terms of matrix refinable functions or vector subdivision schemes, respectively, in order to be suitable for iterated application. Moreover, it is shown for a particular case that the the condition is not only a necessary but also a sufficient one. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1007/s10444-004-7635-y | Adv. Comput. Math. |
Keywords | Field | DocType |
subdivision,refinable function,subconvergence | Refinable function,Mathematical optimization,Mathematical analysis,Matrix (mathematics),Differentiable function,Subdivision,Factorization,Transfer matrix,Subsequence,Iterated function,Mathematics | Journal |
Volume | Issue | ISSN |
25 | 1-3 | 1019-7168 |
Citations | PageRank | References |
6 | 0.87 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Tomas Sauer | 1 | 161 | 30.79 |
| Lehrstuhl für Numerische Mathematik | 2 | 6 | 0.87 |
| Justus-Liebig-Universität Giessen | 3 | 6 | 0.87 |