For any positive integers h >= 2 and g >= 1, we present a greedy algorithm that provides an infinite B-h[g] sequence (a(n))(n)>= 1 with a(n) <= 2gn(h+(h-1)/g). (C) 2017 Published by Elsevier Inc.
For any positive integers h >= 2 and g >= 1, we present a greedy algorithm that provides an infinite B-h[g] sequence (a(n))(n)>= 1 with a(n) <= 2gn(h+(h-1)/g). (C) 2017 Published by Elsevier Inc.
We present a greedy algorithm for computing selected eigenpairs of a large sparse matrixHthat can exploit localization features of the eigenvector. When the eigenvector to be computed is localized, meaning only a smal...
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We present a greedy algorithm for computing selected eigenpairs of a large sparse matrixHthat can exploit localization features of the eigenvector. When the eigenvector to be computed is localized, meaning only a small number of its components have large magnitudes, the proposed algorithm identifies the location of these components in a greedy manner, and obtains approximations to the desired eigenpairs ofHby computing eigenpairs of a submatrix extracted from the corresponding rows and columns ofH. Even when the eigenvector is not completely localized, the approximate eigenvectors obtained by the greedy algorithm can be used as good starting guesses to accelerate the convergence of an iterative eigensolver applied toH. We discuss a few possibilities for selecting important rows and columns ofHand techniques for constructing good initial guesses for an iterative eigensolver using the approximate eigenvectors returned from the greedy algorithm. We demonstrate the effectiveness of this approach with examples from nuclear quantum many-body calculations, many-body localization studies of quantum spin chains and road network analysis.
In this paper, we prove that for any epsilon is an element of(0, 1) there exists ameasurable set E is an element of [0, 1) with measure vertical bar E vertical bar > 1 - epsilon such that for any function f is an e...
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In this paper, we prove that for any epsilon is an element of(0, 1) there exists ameasurable set E is an element of [0, 1) with measure vertical bar E vertical bar > 1 - epsilon such that for any function f is an element of L-1[0, 1), it is possible to construct a function (f) over tilde L1[0,1] coinciding with f on E and satisfying integral(1)(0)vertical bar(f) over tilde (x)-f(x)vertical bar dx greedy algorithm of <(f)over tilde> with respect to a bounded Vilenkin system are almost everywhere convergent on [0, 1).
Starting from the greedy theory, this paper presents a novel adaptive greedy scheme for the power amplifier (PA) behavioral model adaptive pruning. The proposed scheme incorporates the stochastic conjugate gradient (S...
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Starting from the greedy theory, this paper presents a novel adaptive greedy scheme for the power amplifier (PA) behavioral model adaptive pruning. The proposed scheme incorporates the stochastic conjugate gradient (SCG) principle into the subspace pursuit (SP) greedy algorithm, which can considerably offer improved tracking capabilities and faster convergence compared to other anterior adaptive greedy algorithms. Compared to conventional nonsparse methods, simulation results show that the proposed scheme can efficiently reduce the model order and computational complexity but almost have the comparable model performance with the full model. (C) 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.
We consider the problems of the uniform convergence of the greedy algorithm in the generalized Walsh system I (a) , a a parts per thousand yen 2, after correcting a function on a set of small measure.
We consider the problems of the uniform convergence of the greedy algorithm in the generalized Walsh system I (a) , a a parts per thousand yen 2, after correcting a function on a set of small measure.
With continuous advancements in artificial intelligence(AI), automatic piano-playing robots have become subjects of cross-disciplinary interest. However, in most studies, these robots served merely as objects of obser...
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With continuous advancements in artificial intelligence(AI), automatic piano-playing robots have become subjects of cross-disciplinary interest. However, in most studies, these robots served merely as objects of observation with limited user engagement or interaction. To address this issue, we propose a user-friendly and innovative interaction system based on the principles of greedy algorithms. This system features three modules: score management, performance control, and keyboard interactions. Upon importing a custom score or playing a note via an external device, the system performs on a virtual piano in line with user inputs. This system has been successfully integrated into our dexterous manipulator-based piano-playing device, which significantly enhances user interactions.
The article discusses the characteristics of greedy algorithm. It presents various mathematical formula which highlight the Banach and Hilbert spaces. It also stresses the convergence and the rate of convergence of th...
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The article discusses the characteristics of greedy algorithm. It presents various mathematical formula which highlight the Banach and Hilbert spaces. It also stresses the convergence and the rate of convergence of the X-greedy algorithm for a fixed dictionary with functions that are relative to the indicators of binary intervals.
A vector-measurement-sensor problem for the least squares estimation is considered, by extending a previous novel approach in this letter. An extension of the vector-measurement-sensor selection of the greedy algorith...
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A vector-measurement-sensor problem for the least squares estimation is considered, by extending a previous novel approach in this letter. An extension of the vector-measurement-sensor selection of the greedy algorithm is proposed and is applied to particle-image-velocimetry data to reconstruct the full state based on the information given by sparse vector-measurement sensors.
作者：
Steel, MUniv Canterbury
Allan Willson Ctr Mol Ecol & Evolut Biomath Res Ctr Christchurch 1 New Zealand
Given a phylogenetic tree with leaves labeled by a collection of species, and with weighted edges, the "phylogenetic diversity" of any subset of the species is the sum of the edge weights of the minimal subt...
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Given a phylogenetic tree with leaves labeled by a collection of species, and with weighted edges, the "phylogenetic diversity" of any subset of the species is the sum of the edge weights of the minimal subtree connecting the species. This measure is relevant in biodiversity conservation where one may wish to compare different subsets of species according to how much evolutionary variation they encompass. In this note we show that phylogenetic diversity has an attractive mathematical property that ensures that we can solve the following problem easily by the greedy algorithm: find a subset of the species of any given size k of maximal phylogenetic diversity. We also describe an extension of this result that also allows weights to be assigned to species.
In contrast to linear schemes, nonlinear approximation techniques allow for dimension independent rates of convergence. Unfortunately, typical algorithms (such as, e.g., backpropagation) are not only computationally d...
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In contrast to linear schemes, nonlinear approximation techniques allow for dimension independent rates of convergence. Unfortunately, typical algorithms (such as, e.g., backpropagation) are not only computationally demanding, but also unstable in the presence of data noise. While we can show stability for a weak relaxed greedy algorithm, the resulting method has the drawback that it requires in practise unavailable smoothness information about the data. In this work we propose an adaptive greedy algorithm which does not need this information but rather recovers it iteratively from the available data. We show that the generated approximations are always at least as smooth as the original function and that the algorithm also remains stable, when it is applied to noisy data. Finally, the applicability of this algorithm is demonstrated by numerical experiments. (c) 2006 ***. All rights reserved.
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