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A class of globally convergent conjugate gradient methods

Science China Mathematics 2003年第2期46卷 251-261页

作者：戴彧虹袁亚湘 State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences

Conjugate gradient methods are very important ones for solving nonlinear optimization problems,especially for large scale problems. However, unlike quasi-Newton methods, conjugate gradient methods wereusually analyzed individually. In this paper, we propose a class of conjugate gradient methods, which can beregarded as some kind of convex combination of the Fletcher-Reeves method and the method proposed byDai et al. To analyze this class of methods, we introduce some unified tools that concern a general methodwith the scalarβk having the form of φk/φk-1. Consequently, the class of conjugate gradient methods canuniformly be analyzed.

关键词： unconstrained optimization, conjugate gradient, line search, global convergence.

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ON THE CONVERGENCE DOMAIN OF THE MATRIX MULTISPLITTING RELAXATION METHODS FOR LINEAR SYSTEMS

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Applied Mathematics(A Journal of Chinese Universities) 1998年第1期13卷 45-52页

作者： BAI ZHONGZHI State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of Science Beijing

The convergence of the parallel matrix multisplitting relaxation methods presented by Wang (Linear Algebra and Its Applications 154/156 (1991) 473 486) is further investigated. The investigations show that these relax... 详细信息

关键词： System of linear equations matrix multisplitting convergence domain.

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Understanding urban structures and crowd dynamics leveraging large-scale vehicle mobility data

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Frontiers of Computer Science 2020年第5期14卷 77-88页

作者： Zhihan Jiang Yan Liu Xiaoliang Fan Cheng Wang Jonathan Li Longbiao Chen Fujian Key Laboratory of Sensing and Computing for Smart Cities School of Information Science and EngineeringXiamen UniversityXiamen361005China

A comprehensive understanding of city structures and urban dynamics can greatly improve the efficiency and quality of urban planning and management,while the traditional approaches of which,such as manual surveys,usually incur substantial labor and *** this paper,we propose a data-driven framework to sense urban structures and dynamics from large-scale vehicle mobility ***,we divide the city into fine-grained grids,and cluster the grids with similar mobility features into structured urban areas with a proposed distance-constrained clustering algorithm(DCCA).Second,we detect irregular mobility traffic patterns in each area leveraging an ARIMA-based anomaly detection algorithm(ADAM),and correlate them to the urban social and emergency ***,we build a visualization system to demonstrate the urban structures and crowd *** evaluate our framework using real-world datasets collected from Xiamen city,China,and the results show that the proposed framework can sense urban structures and crowd comprehensively and effectively.

关键词： vehicle mobility big data spatial clustering event detection urban computing ubiquitous computing

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VOLUME-PRESERVING SCHEMES AND APPLICATIONS

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CHAOS SOLITONS & FRACTALS 1993年第6期3卷 637-649页

作者： QIN, MZ ZHU, WJ State Key Laboratory of Scientific and Engineering Computing Center Academia Sinica Beijing 100080 PR China

In this paper, we discuss the conditions for the Euler midpoint rule to be volume-preserving and present Euler type explicit volume-preserving schemes. Some numerical applications to the system defining rigid body mot... 详细信息

关键词： Systems analysis

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Convergence properties of the Fletcher-Reeves method

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IMA JOURNAL OF NUMERICAL ANALYSIS 1996年第2期16卷 155-164页

作者： Dai, YH Yuan, Y State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of SciencesPO Box 2719 Beijing 100080 People's Republic of China

This paper investigates the global convergence properties of the Fletcher-Reeves (FR) method for unconstrained optimization. In a simple way, we prove that a kind of inexact line search condition can ensure the convergence of the FR method. Several examples are constructed to show that, if the search conditions are relaxed, the FR method may produce an ascent search direction, which implies that our result cannot be improved.

关键词： Optimization

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Learning with Noisy Labels: the Exploration of Error Bounds in Classification

arXiv

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arXiv 2025年

作者： Liu, Haixia Li, Boxiao Yang, Can Wang, Yang School of Mathematics and Statistics Institute of Interdisciplinary Research for Mathematics and Applied Science Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan China School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Wuhan China Department of Mathematics The Hong Kong University of Science and Technology Clear Water Bay China

Numerous studies have shown that label noise can lead to poor generalization performance, negatively affecting classification accuracy. Therefore, understanding the effectiveness of classifiers trained using deep neural networks in the presence of noisy labels is of considerable practical significance. In this paper, we focus on the error bounds of excess risks for classification problems with noisy labels within deep learning frameworks. We begin by exploring loss functions with noise-tolerant properties, ensuring that the empirical minimizer on noisy data aligns with that on the true data. Next, we estimate the error bounds of the excess risks, expressed as a sum of statistical error and approximation error. We estimate the statistical error on a dependent (mixing) sequence, bounding it with the help of the associated independent block sequence. For the approximation error, we first express the classifiers as the composition of the softmax function and a continuous function from [0, 1]d to RK. The main task is then to estimate the approximation error for the continuous function from [0, 1]d to RK. Finally, we focus on the curse of dimensionality based on the low-dimensional manifold assumption. Copyright © 2025, The Authors. All rights reserved.

关键词： Risk assessment

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Sensing With Communication Signals: From Information Theory to Signal Processing

arXiv

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arXiv 2025年

作者： Liu, Fan Liu, Ya-Feng Cui, Yuanhao Masouros, Christos Xu, Jie Han, Tony Xiao Buzzi, Stefano Eldar, Yonina C. Jin, Shi National Mobile Communications Research Laboratory School of Information Science and Engineering Southeast University Nanjing210096 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematicsand Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Department of Communication Engineering Beijing University of Posts and Telecommunications Beijing100876 China Department of Electronic and Electrical Engineering University College London LondonWC1E 7JE United Kingdom Guangdong518172 China Huawei Technologies Co. Ltd China Department of Electrical and Information Engineering University of Cassino and Southern Lazio CassinoI-03043 Italy Department of Electronics Information and Bioengineering Politecnico di Milano MilanoI-20133 Italy ParmaI-43124 Italy Faculty of Mathematics and Computer Science Weizmann Institute of Science Rehovot Israel

The Integrated Sensing and Communications (ISAC) paradigm is anticipated to be a cornerstone of the upcoming 6G networks. In order to optimize the use of wireless resources, 6G ISAC systems need to harness the communication data payload signals, which are inherently random, for both sensing and communication (S&C) purposes. This tutorial paper provides a comprehensive technical overview of the fundamental theory and signal processing methodologies for ISAC transmission with random communication signals. We begin by introducing the deterministic-random tradeoff (DRT) between S&C from an information-theoretic perspective, emphasizing the need for specialized signal processing techniques tailored to random ISAC signals. Building on this foundation, we review the core signal models and processing pipelines for communication-centric ISAC systems, and analyze the average squared auto-correlation function (ACF) of random ISAC signals, which serves as a fundamental performance metric for multi-target ranging tasks. Drawing insights from these theoretical results, we outline the design principles for the three key components of communication-centric ISAC systems: modulation schemes, constellation design, and pulse shaping filters. The goal is to either enhance sensing performance without compromising communication efficiency or to establish a scalable tradeoff between the two. We then extend our analysis from a single-antenna ISAC system to its multi-antenna counterpart, discussing recent advancements in multiinput multi-output (MIMO) precoding techniques specifically designed for random ISAC signals. We conclude by highlighting several open challenges and future research directions in the field of sensing with communication signals. Copyright © 2025, The Authors. All rights reserved.

关键词： Signal modulation

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ON INTEGRABILITY UP TO THE BOUNDARY OF THE WEAK SOLUTIONS TO A NON-NEWTONIAN FLUID

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Acta Mathematica Scientia 2019年第2期39卷 420-428页

作者： Shanshan GUO Zhong TAN School of Mathematical Sciences Xiamen University School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and Scientific Computing Xiamen University

This work consider boundary integrability of the weak solutions of a non-Newtonian compressible fluids in a bounded domain in dimension three, which has the constitutive equartions as ■The existence result of weak solutions can be get based on Galerkin approximation. With the linear operator B constructed by BOGOVSKII, we show that the density ■is square integrable up to the boundary.

关键词： compressible fluid weak solutions non-Newtonian fluids integrability

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HIGH ORDER FINITE DIFFERENCE/SPECTRAL METHODS TO A WATER WAVE MODEL WITH NONLOCAL VISCOSITY

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Journal of Computational Mathematics 2020年第4期38卷 580-605页

作者： Mohammad Tanzil Hasan Chuanju Xu School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing Xiamen UniversityXiamen 361005China

In this paper,efficient numerical scheme is proposed for solving the water wave model with nonlocal viscous term that describe the propagation of surface water *** using the Caputo fractional derivative definition to approximate the nonlocal fractional operator,finite difference method in time and spectral method in space are constructed for the considered *** proposed method employs known 5/2 order scheme for fractional derivative and a mixed linearization for the nonlinear *** analysis shows that the proposed numerical scheme is unconditionally stable and error estimates are provided to predict that the second order backward differentiation plus 5/2 order scheme converges with order 2 in time,and spectral accuracy in *** numerical results are provided to verify the efficiency and accuracy of our theoretical ***,the decay rate of solutions are investigated.

关键词： Water waves Nonlocal viscosity Finite difference Spectral method Conver-gence order Decay rate

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Weighted Density for The Win: Accurate Subspace Density Clustering

Weighted Density for The Win: Accurate Subspace Density Clus...

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International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Maixuan Peng Yuyang Wu Yang Lu Mengke Li Yiqun Zhang Yiu-Ming Cheung School of Computer Science and Technology Guangdong University of Technology Guangzhou China Faculty of Science Wilfrid Laurier University Brantford Canada Fujian Key Laboratory of Sensing and Computing for Smart City School of Informatics Xiamen University Xiamen China College of Computer Science and Software Engineering Shenzhen University Shenzhen China Department of Computer Science Hong Kong Baptist University China

ISBN: (数字)9798350368741

ISBN: (纸本)9798350368758

k-clustering typically struggles with the detection of irregular-distributed clusters due to the natural bias, while density clustering usually cannot well-adapt to different datasets and clustering tasks as it is not an oriented optimization process. This paper, therefore, proposes to perform density clustering in dynamically learned subspaces. To exploit the irregular-distributed clusters obtained by density clustering for the subspace determination, we design a new strategy to appropriately evaluate the importance of attributes. It turns out that the proposed Weighted Density-based Subspace Clustering (WDSC) algorithm inherits the unbiased merits of density clustering, and also upgrades the unlearning density clustering to be learnable under the subspace learning paradigm of k-clustering. A comprehensive evaluation including significance tests, ablation studies, qualitative comparisons, etc., shows the superiority of WDSC.

关键词： Accuracy Heuristic algorithms Signal processing algorithms Clustering algorithms Signal processing Acoustics Speech processing Optimization

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