共查询到20条相似文献,搜索用时 15 毫秒
1.
Ronald DeVore Guergana Petrova Przemyslaw Wojtaszczyk 《Constructive Approximation》2013,37(3):455-466
Given a Banach space X and one of its compact sets $\mathcal{F}$ , we consider the problem of finding a good n-dimensional space X n ?X which can be used to approximate the elements of $\mathcal{F}$ . The best possible error we can achieve for such an approximation is given by the Kolmogorov width $d_{n}(\mathcal{F})_{X}$ . However, finding the space which gives this performance is typically numerically intractable. Recently, a new greedy strategy for obtaining good spaces was given in the context of the reduced basis method for solving a parametric family of PDEs. The performance of this greedy algorithm was initially analyzed in Buffa et al. (Modél. Math. Anal. Numér. 46:595–603, 2012) in the case $X=\mathcal{H}$ is a Hilbert space. The results of Buffa et al. (Modél. Math. Anal. Numér. 46:595–603, 2012) were significantly improved upon in Binev et al. (SIAM J. Math. Anal. 43:1457–1472, 2011). The purpose of the present paper is to give a new analysis of the performance of such greedy algorithms. Our analysis not only gives improved results for the Hilbert space case but can also be applied to the same greedy procedure in general Banach spaces. 相似文献
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Geographic Routing is a family of routing algorithms that uses geographic point locations as addresses for the purposes of routing. Such routing algorithms have proven to be both simple to implement and heuristically effective when applied to wireless sensor networks. Greedy Routing is a natural abstraction of this model in which nodes are assigned virtual coordinates in a metric space, and these coordinates are used to perform point-to-point routing. 相似文献
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We prove that the Banach space (?n=1¥lpn)lq(\bigoplus_{n=1}^{\infty}\ell_{p}^{n})_{\ell_{q}}, which is isomorphic to certain Besov spaces, has a greedy basis whenever 1≤p≤∞ and 1<q<∞. Furthermore, the Banach spaces (?n=1¥lpn)l1(\bigoplus_{n=1}^{\infty}\ell _{p}^{n})_{\ell_{1}}, with 1<p≤∞, and (?n=1¥lpn)c0(\bigoplus_{n=1}^{\infty}\ell_{p}^{n})_{c_{0}}, with 1≤p<∞, do not have a greedy basis. We prove as well that the space (?n=1¥lpn)lq(\bigoplus_{n=1}^{\infty}\ell _{p}^{n})_{\ell_{q}} has a 1-greedy basis if and only if 1≤p=q≤∞. 相似文献
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We study the convergence of greedy algorithms in Banach spaces. We construct an example of a smooth Banach space, where the X-greedy algorithm converges not for all dictionaries and initial vectors. We also study the R-greedy algorithm, which, along with the X-greedy algorithm, is a generalization of the simple greedy algorithm in Hilbert space. We prove its convergence for a certain class of Banach spaces. In particular, this class contains, the spaces p,p 2. 相似文献
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S.J. Dilworth Denka Kutzarova V.N. Temlyakov 《Journal of Fourier Analysis and Applications》2002,8(5):489-506
We consider some theoretical greedy algorithms for approximation in Banach spaces with respect to a general dictionary. We prove convergence of the algorithms for Banach spaces which satisfy certain smoothness assumptions. We compare the algorithms and their rates of convergence when the Banach space is Lp(\mathbbTd)L_p(\mathbb{T}^d) ($1
相似文献
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本文首先在 Banach空间上引入了 N-框架与 M-Riesz基 .给出 N-框架的充要条件和 N-框架与 M-Riesz基的关系 ,其中 M,N为 Orlicz函数 ,再讨论它们的稳定性 相似文献
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朱玉灿 《数学物理学报(A辑)》2001,21(Z1):655-664
该文首先给出Banach空间上的框架与拟Riesz基的充要条件,其次讨论Banach空间上的框架和拟Riesz基的稳定性,特别地,讨论在Banach空间上关于框架与拟Riesz基的广义Paley Wiener定理. 相似文献
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S. J. Dilworth Denka Kutzarova Karen L. Shuman V. N. Temlyakov P. Wojtaszczyk 《Journal of Fourier Analysis and Applications》2008,14(5-6):609-628
We study the convergence of certain greedy algorithms in Banach spaces. We introduce the WN property for Banach spaces and prove that the algorithms converge in the weak topology for general dictionaries in uniformly smooth Banach spaces with the WN property. We show that reflexive spaces with the uniform Opial property have the WN property. We show that our results do not extend to algorithms which employ a ‘dictionary dual’ greedy step. 相似文献
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Eugenio Hern��ndez Jos�� Mar��a Martell Maria de Natividade 《Constructive Approximation》2011,33(1):1-14
We study the efficiency of the greedy algorithm for wavelet bases in Lorentz spaces in order to give the near best approximation.
The result is used to give sharp inclusions for the approximation spaces in terms of discrete Lorentz sequence spaces. 相似文献
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In spline spaces there are often totally positive bases possessing a strong property called almost strictly total positivity. In this paper, it is proved that, for totally positive bases of continuous functions B, the following concepts are equivalent: (i) B is almost strictly totally positive, (ii) B satifies a Schoenberg-Whitney Theorem, (iii) The functions in B are locally linearly independent. Some classical examples of almost strictly totally positive bases are given, completing the knowledge of their properties known in the mathematical literature. Some criteria to know the existence of almost strictly totally positive bases are also derived. 相似文献
13.
Let A and B be countable discrete groups, and let = A * B betheir free product. We show that if A and B are uniformly embeddableinto a uniformly convex Banach space, then so is . 2000 MathematicsSubject Classification 46L89, 20F65. 相似文献
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George Androulakis Alexey I. Popov Adi Tcaciuc Vladimir G. Troitsky 《Integral Equations and Operator Theory》2009,65(4):473-484
We introduce and study the following modified version of the Invariant Subspace Problem: whether every operator T on an infinite-dimensional Banach space has an almost invariant half-space, that is, a subspace Y of infinite dimension and infinite codimension such that Y is of finite codimension in T(Y). We solve this problem in the affirmative for a large class of operators which includes quasinilpotent weighted shift operators
on ℓp (1 ≤ p < ∞) or c0. 相似文献
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Computational Mathematics and Mathematical Physics - The paper studies weak greedy algorithms for finding sparse solutions of convex optimization problems in Banach spaces. We consider the concept... 相似文献
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Johnson William B.; Lindenstrauss Joram; Preiss David; Schechtman Gideon 《Proceedings London Mathematical Society》2002,84(3):711-746
We give several sufficient conditions on a pair of Banach spacesX and Y under which each Lipschitz mapping from a domain inX to Y has, for every > 0, a point of -Fréchet differentiability.Most of these conditions are stated in terms of the moduli ofasymptotic smoothness and convexity, notions which have appearedin the literature under a variety of names. We prove, for example,that for > r > p 1, every Lipschitz mapping from a domainin an lr-sum of finite-dimensional spaces into an lp-sum offinite-dimensional spaces has, for every > 0, a point of-Fréchet differentiability, and that every Lipschitzmapping from an asymptotically uniformly smooth space to a finite-dimensionalspace has such points. The latter result improves, with a simplerproof, an earlier result of the second and third authors. Wealso survey some of the known results on the notions of asymptoticsmoothness and convexity, prove some new properties, and presentsome new proofs of existing results. 2000 Mathematical Subject Classification: 46G05, 46T20. 相似文献
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本文首先在Banach空间引入了N-框架与M-Riesz基。给出N-框架的充要条件和N-框架与M-Riesz基的关系,其中M,N为Orilicz函数,再讨论它们的稳定性。 相似文献
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本文定义了几乎第二可数空间,几乎第一数可空间和几乎可分空间,它们分别是第二可数空间,第一可数空间和可分空间的一般化,还研究了这三类新空间以及几乎Lindel?f空间的性质,改进了[2]中的几个定理. 相似文献