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We study greedy approximation in uniformly smooth Banach spaces. The Weak Chebyshev Greedy Algorithm (WCGA), introduced and studied in [6], is defined for any Banach space X and a dictionary D, and… (More)

A unified way of analyzing different greedy-type algorithms in Banach spaces is presented. We define a class of Weak Biorthogonal Greedy Algorithms and prove convergence and rate of convergence… (More)

The following two types of greedy algorithms are considered: the pure greedy algorithm (PGA) and the orthogonal greedy algorithm (OGA). From the standpoint of estimating the rate of convergence on… (More)

In this dissertation we study the questions of convergence and rate of convergence of greedy-type algorithms under imprecise step evaluations. Such algorithms are in demand as the issue of… (More)

The goal of a reduced basis method is to find an approximating subspace for a given set of data. In this paper we mainly consider a recursive greedy approach for constructing such subspaces. We… (More)

The Weak Chebyshev Greedy Algorithm (WCGA) is defined for any Banach space X and a dictionary D, and provides nonlinear n-term approximation for a given element f ∈ X with respect to D. In this paper… (More)

We present a novel greedy approach to obtain a single layer neural network approximation to a target function with the use of a ReLU activation function. In our approach we construct a shallow… (More)

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