Convergence of nonstationary cascade algorithms
| العنوان: | Convergence of nonstationary cascade algorithms |
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| المؤلفون: | Seng Luan Lee, Tim N. T. Goodman |
| المصدر: | Numerische Mathematik. 84:1-33 |
| بيانات النشر: | Springer Science and Business Media LLC, 1999. |
| سنة النشر: | 1999 |
| مصطلحات موضوعية: | Dilation matrix, Discrete mathematics, Combinatorics, Computational Mathematics, Transition operator, Cascade, Applied Mathematics, Spectral properties, Convergence (routing), Cascade algorithm, Mathematics |
| الوصف: | A nonstationary multiresolution of $L^2(\mathbb{R}^s)$ is generated by a sequence of scaling functions $\phi_k\in L^2(\mathbb{R}^s), k\in \mathbb{Z}.$ We consider $(\phi_k)$ that is the solution of the nonstationary refinement equations $\phi_k = |M|$ $ \sum_{j} h_{k+1}(j)\phi_{k+1}(M \cdot -j), k\in \mathbb{Z},$ where $h_k$ is finitely supported for each k and M is a dilation matrix. We study various forms of convergence in $L^2(\mathbb{R}^s)$ of the corresponding nonstationary cascade algorithm $\phi_{k,n} = |M| \sum_{j} h_{k+1}(j)\phi_{k+1,n-1}(M \cdot -j),$ as k or n tends to $\infty.$ It is assumed that there is a stationary refinement equation at $\infty$ with filter sequence h and that $\sum_k |h_k(j) - h(j)| < \infty.$ The results show that the convergence of the nonstationary cascade algorithm is determined by the spectral properties of the transition operator associated with h. |
| تدمد: | 0945-3245 0029-599X |
| DOI: | 10.1007/s002110050462 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::bd7b93c1685dd8c5b5e386ded4bc0b61 https://doi.org/10.1007/s002110050462 |
| Rights: | CLOSED |
| رقم الانضمام: | edsair.doi...........bd7b93c1685dd8c5b5e386ded4bc0b61 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 09453245 0029599X |
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| DOI: | 10.1007/s002110050462 |