Related papers: Lebesgue inequalities for the greedy algorithm in …

We establish estimates for the Lebesgue parameters of the Chebyshev Weak Thresholding Greedy Algorithm in the case of general bases in Banach spaces. These generalize and slightly improve earlier results in [9], and are complemented with…

We obtain Lebesgue-type inequalities for the greedy algorithm for arbitrary complete seminormalized biorthogonal systems in Banach spaces. The bounds are given only in terms of the upper democracy functions of the basis and its dual. We…

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…

The purpose of this paper is to quantify the size of the Lebesgue constants $(L_m)_{m=1}^{\infty}$ associated with the thresholding greedy algorithm in terms of a new generation of parameters that modulate accurately some features of a…

We continue the study of Lebesgue-type parameters for various greedy algorithms in quasi-Banach spaces. First, we introduce a parameter that can be used with the quasi-greedy parameter to obtain the exact growth of the Lebesgue parameter…

In this paper we continue the study of Lebesgue-type inequalities for greedy algorithms. We introduce the notion of strong partially greedy Markushevich bases and study the Lebesgue-type parameters associated with them. We prove that this…

Greedy algorithms are a fundamental category of algorithms in mathematics and computer science, characterized by their iterative, locally optimal decision-making approach, which aims to find global optima. In this review, we will discuss…

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…

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…

In this paper we study greedy approximation in Banach spaces. We discuss a modification of the Weak Chebyshev Greedy Algorithm, in which steps of the algorithm can be executed imprecisely. Such inaccuracies are represented by both absolute…

We present new results regarding Lebesgue-type inequalities for the Weak Chebyshev Greedy Algorithm (WCGA) in uniformly smooth Banach spaces. We improve earlier bounds in Temlyakov (Forum Math Sigma 2014), for dictionaries satisfying a new…

We study sparse approximation by greedy algorithms. We prove the Lebesgue-type inequalities for the Weak Chebyshev Greedy Algorithm (WCGA), a generalization of the Weak Orthogonal Matching Pursuit to the case of a Banach space. The main…

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…

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…

Chebyshev Greedy Algorithm is a generalization of the well known Orthogonal Matching Pursuit defined in a Hilbert space to the case of Banach spaces. We apply this algorithm for constructing sparse approximate solutions (with respect to a…

The general theory of greedy approximation with respect to arbitrary dictionaries is well developed in the case of real Banach spaces. Recently, some of results proved for the Weak Chebyshev Greedy Algorithm (WCGA) in the case of real…

We suggest a new greedy strategy for convex optimization in Banach spaces and prove its convergent rates under a suitable behavior of the modulus of uniform smoothness of the objective function.

In this paper we propose a unified way of analyzing a certain kind of greedy-type algorithms in Banach spaces. We define a class of the Weak Biorthogonal Greedy Algorithms that contains a wide range of greedy algorithms. In particular, we…

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…

Greedy algorithms which use only function evaluations are applied to convex optimization in a general Banach space $X$. Along with algorithms that use exact evaluations, algorithms with approximate evaluations are treated. A priori upper…