Weak Convergence of Greedy Algorithms in Banach Spaces
نویسندگان
چکیده
منابع مشابه
Weak Thresholding Greedy Algorithms in Banach Spaces
We consider weak thresholding greedy algorithms with respect to Markushevich bases in general Banach spaces. We find sufficient conditions for the equivalence of boundedness and convergence of the approximants. We also show that if there is a weak thresholding algorithm for the system which gives the best n-term approximation up to a multiplicative constant, then the system is already “greedy”....
متن کاملConvergence of the dual greedy algorithm in Banach spaces
We show convergence of the weak dual greedy algorithm in wide class of Banach spaces, extending our previous result where it was shown to converge in subspaces of quotients of Lp (for 1 < p < ∞). In particular, we show it converges in the Schatten ideals Sp when 1 < p < ∞ and in any Banach lattice which is p-convex and q-concave with constants one, where 1 < p < q < ∞. We also discuss convergen...
متن کاملConvergence of the weak dual greedy algorithm in Lp-spaces
We prove that the weak dual greedy algorithm converges in any subspace of a quotient of Lp when 1opoN: r 2003 Elsevier Inc. All rights reserved. A subset D of a (real) Banach space X is called a dictionary if (i) D is normalized i.e. if gAD implies jjgjj 1⁄4 1: (ii) D is symmetric i.e. D 1⁄4 D: (iii) D is fundamental i.e. 1⁄2D 1⁄4 X : Given xAX we are interested in algorithms which generate a s...
متن کاملGreedy Algorithms for Reduced Bases in Banach Spaces∗
Given a Banach space X and one of its compact sets F , we consider the problem of finding a good n dimensional space Xn ⊂ X which can be used to approximate the elements of F . The best possible error we can achieve for such an approximation is given by the Kolmogorov width dn(F)X . However, finding the space which gives this performance is typically numerically intractable. Recently, a new gre...
متن کاملWeak convergence theorems for symmetric generalized hybrid mappings in uniformly convex Banach spaces
In this paper, we prove some theorems related to properties of generalized symmetric hybrid mappings in Banach spaces. Using Banach limits, we prove a fixed point theorem for symmetric generalized hybrid mappings in Banach spaces. Moreover, we prove some weak convergence theorems for such mappings by using Ishikawa iteration method in a uniformly convex Banach space.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Fourier Analysis and Applications
سال: 2008
ISSN: 1069-5869,1531-5851
DOI: 10.1007/s00041-008-9034-0