论文标题
稀疏的近似，使用超级反射空间中的新型贪婪的基础
Sparse approximation using new greedy-like bases in superreflexive spaces
论文作者
论文摘要
本文致力于稀疏近似最佳性的理论方面。我们对最近在Banach空间中非线性$ m $ - 期限近似的背景下出现的新型贪婪基础进行了定量研究，作为对几乎贪婪基础的特征的概括，即准式和民主。为了将这些新基础的效率与已经存在的阈值贪婪算法的效率进行比较，我们将重点放在获得其无条件参数顺序的估计上。使用[S. J. Dilworth，N。J。Kalton和D. Kutzarova，关于Banach空间中几乎贪婪的基础，Studia Math。 159（2003），否。 1，67-101]为了建立几乎贪婪的基础，我们设法构建了双民主基础，其无条件参数的估计明显比希尔伯特空间中的几乎贪婪基础要差得多。
This paper is devoted to theoretical aspects on optimality of sparse approximation. We undertake a quantitative study of new types of greedy-like bases that have recently arisen in the context of nonlinear $m$-term approximation in Banach spaces as a generalization of the properties that characterize almost greedy bases, i.e., quasi-greediness and democracy. As a means to compare the efficiency of these new bases with already existing ones in regards to the implementation of the Thresholding Greedy Algorithm, we place emphasis on obtaining estimates for their sequence of unconditionality parameters. Using an enhanced version of the original method from [S. J. Dilworth, N. J. Kalton, and D. Kutzarova, On the existence of almost greedy bases in Banach spaces, Studia Math. 159 (2003), no. 1, 67-101] for building almost greedy bases, we manage to construct bidemocratic bases whose unconditionality parameters satisfy significantly worse estimates than almost greedy bases even in Hilbert spaces.
