Related papers: On sequential greedy-type bases
In this paper we show that that greedy bases can be defined as those where the error term using $m$-greedy approximant is uniformly bounded by the best $m$-term approximation with respect to polynomials with constant coefficients in the…
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…
Elton's near unconditionality and quasi-greediness for largest coefficients are two properties of bases that made their appearance in functional analysis from very different areas of research. One of our aims in this note is to show that,…
We show that for quasi-greedy bases in real Banach spaces the error of the thresholding greedy algorithm of order N is bounded by the best N-term error of approximation times a constant which depends on the democracy functions and the…
We investigate various aspects of the "weighted" greedy algorithm with respect to a Schauder basis. For a weight w, we describe w-greedy, w-almost-greedy and w-partially-greedy bases, and show some properties of w-semi-greedy bases. To…
Greedy bases are those bases where the Thresholding Greedy Algorithm (introduced by S. V. Konyagin and V. N. Temlyakov) produces the best possible approximation up to a constant. In 2017, Bern\'a and Blasco gave a characterization of these…
In 2003, S. J. Dilworth et al. ([8]) introduced the notion of almost-greedy (resp. partially-greedy) bases. These bases were characterized in terms of quasi-greediness and democracy (resp. conservativeness). In this paper we will show a new…
We prove some results on the rate of convergence of greedy algorithms, which provide expansions. We consider both the case of Hilbert spaces and the more general case of Banach spaces. The new ingredient of the paper is that we bound the…
The general problem addressed in this work is the development of a systematic study of the thresholding greedy algorithm for general biorthogonal systems (also known as Markushevich bases) in quasi-Banach spaces from a functional-analytic…
We study greedy-type algorithms such that at a greedy step we pick several dictionary elements contrary to a single dictionary element in standard greedy-type algorithms. We call such greedy algorithms {\it super greedy algorithms}. The…
We introduce and study the notion of weak semi-greedy systems -which is inspired in the concepts of semi-greedy and Branch semi-greedy systems and weak thresholding sets-, and prove that in the context Markushevich bases in infinite…
We show that for quasi-greedy bases in real or complex Banach spaces the error of the thresholding greedy algorithm of order N is bounded by the best N- term error of approximation times a function of N which depends on the democracy…
For the past 25 years, one of the most studied algorithms in the field of Nonlinear Approximation Theory has been the Thresholding Greedy Algorithm. In this paper, we propose new summability methods for this algorithm, generating two new…
We characterize the approximation spaces of a broad class of bases - which includes almost greedy bases - in terms of weighted Lorentz spaces. For those bases, we also find necessary and sufficient conditions under which the approximation…
Property~(A) is a week symmetry condition that plays a fundamental role in the characterization of greedy-type bases in the isometric case, i.e., when the constants involved in the study of the efficiency of the thresholding greedy…
We study the greedy (exploitation-only) algorithm in bandit problems with a known reward structure. We allow arbitrary finite reward structures, while prior work focused on a few specific ones. We fully characterize when the greedy…
In this paper, we establish new advances in the theory started by T. Oikhberg in [15] where the author joins greedy approximation theory with the use of sequences with gaps. Concretely, we address and partially answer three open questions…
The change-making problem consists of representing a certain amount of money with the least possible number of coins, from a given, pre-established set of denominations. The greedy algorithm works by choosing the coins of largest possible…
We propose a new concept named adaptive submodularity ratio to study the greedy policy for sequential decision making. While the greedy policy is known to perform well for a wide variety of adaptive stochastic optimization problems in…
In this paper, we study greedy variants of quasi-Newton methods. They are based on the updating formulas from a certain subclass of the Broyden family. In particular, this subclass includes the well-known DFP, BFGS and SR1 updates. However,…