检索结果-内蒙古大学图书馆

arXiv 2020年

作者： Wang, Haiyong School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

Motivated by comparing the convergence behavior of Gegenbauer projections and best approximations, we study the optimal rate of convergence for Gegenbauer projections in the maximum norm. We show that the rate of convergence of Gegenbauer projections is the same as that of best approximations under conditions of the underlying function is either analytic on and within an ellipse and λ ≤ 0 or differentiable and λ ≤ 1, where λ is the parameter in Gegenbauer projections. If the underlying function is analytic and λ > 0 or differentiable and λ > 1, then the rate of convergence of Gegenbauer projections is slower than that of best approximations by factors of nλ and nλ−1, respectively. An exceptional case is functions with endpoint singularities, for which Gegenbauer projections and best approximations converge at the same rate for all λ > −1/2. For functions with interior or endpoint singularities, we provide a theoretical explanation for the error localization phenomenon of Gegenbauer projections and for why the accuracy of Gegenbauer projections is better than that of best approximations except in small neighborhoods of the critical points. Our analysis provides fundamentally new insight into the power of Gegenbauer approximations and related spectral *** Codes 41A10, 41A25 Copyright © 2020, The Authors. All rights reserved.

关键词： Functions

来源：评论

学校读者我要写书评

暂无评论

How much faster does the best polynomial approximation converge than Legendre projection?

arXiv

引用

arXiv 2020年

We compare the convergence behavior of best polynomial approximations and Legendre and Chebyshev projections and derive optimal rates of convergence of Legendre projections for analytic and differentiable functions in the maximum norm. For analytic functions, we show that the best polynomial approximation of degree n is better than the Legendre projection of the same degree by a factor of n1/2. For differentiable functions such as piecewise analytic functions and functions of fractional smoothness, however, we show that the best approximation is better than the Legendre projection by only some constant factors. Our results provide some new insights into the approximation power of Legendre projections. Copyright © 2020, The Authors. All rights reserved.

关键词： Functions

来源：评论

学校读者我要写书评

暂无评论

Discrete unified gas kinetic scheme for nonlinear convection-diffusion equations

引用

Physical Review E 2020年第2期101卷 023306-023306页

作者： Jinlong Shang Zhenhua Chai Huili Wang Baochang Shi School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China School of Mathematics and Computer Science Wuhan Textile University Wuhan 430073 China

In this paper, we develop a discrete unified gas kinetic scheme (DUGKS) for a general nonlinear convection-diffusion equation (NCDE) and show that the NCDE can be recovered correctly from the present model through the Chapman-Enskog analysis. We then test the present DUGKS through some classic convection-diffusion equations, and we find that the numerical results are in good agreement with analytical solutions and that the DUGKS model has a second-order convergence rate. Finally, as a finite-volume method, the DUGKS can also adopt the nonuniform mesh. Besides, we perform some comparisons among the DUGKS, the finite-volume lattice Boltzmann model (FV-LBM), the single-relaxation-time lattice Boltzmann model (SLBM), and the multiple-relaxation-time lattice Boltzmann model (MRT-LBM). The results show that the present DUGKS is more accurate than the FV-LBM, more stable than the SLBM, and almost has the same accuracy as the MRT-LBM. Moreover, the use of nonuniform mesh may make the DUGKS model more flexible.

关键词： Lattice-Boltzmann methods

来源：评论

学校读者我要写书评

暂无评论

Make regularization effective in training sparse CNN

引用

Computational Optimization and Applications 2020年第1期77卷 163-182页

作者： He, Juncai Jia, Xiaodong Xu, Jinchao Zhang, Lian Zhao, Liang Department of Mathematics Pennsylvania State University University Park USA Department of Computer Science and Engineering Pennsylvania State University University Park USA State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences and University of Chinese Academy of Sciences Beijing China

Compressed Sensing using $$\ell _1$$ regularization is among the most powerful and popular sparsification technique in many applications, but why has it not been used to obtain sparse deep learning model such as convolutional neural network (CNN)? This paper is aimed to provide an answer to this question and to show how to make it work. Following Xiao (J Mach Learn Res 11(Oct):2543–2596, 2010), We first demonstrate that the commonly used stochastic gradient decent and variants training algorithm is not an appropriate match with $$\ell _1$$ regularization and then replace it with a different training algorithm based on a regularized dual averaging (RDA) method. The RDA method of Xiao (J Mach Learn Res 11(Oct):2543–2596, 2010) was originally designed specifically for convex problem, but with new theoretical insight and algorithmic modifications (using proper initialization and adaptivity), we have made it an effective match with $$\ell _1$$ regularization to achieve a state-of-the-art sparsity for the highly non-convex CNN compared to other weight pruning methods without compromising accuracy (achieving 95% sparsity for ResNet-18 on CIFAR-10, for example).

关键词：

来源：评论

学校读者我要写书评

暂无评论

Optimal network slicing for service-oriented networks with flexible routing and guaranteed E2E latency

arXiv

引用

arXiv 2020年

作者： Chen, Wei-Kun Liu, Ya-Feng de Domenico, Antonio Luo, Zhi-Quan Dai, Yu-Hong The School of Mathematics and Statistics Beijing Key Laboratory on MCAACI Beijing Institute of Technology Beijing100081 China The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The Huawei Technologies Co. Ltd France Research Center Boulogne-Billancourt92100 France The Shenzhen Research Institute of Big Data The Chinese University of Hong Kong Shenzhen518172 China

Network function virtualization is a promising technology to simultaneously support multiple services with diverse characteristics and requirements in the 5G and beyond networks. In particular, each service consists of a predetermined sequence of functions, called service function chain (SFC), running on a cloud environment. To make different service slices work properly in harmony, it is crucial to appropriately select the cloud nodes to deploy the functions in the SFC and flexibly route the flow of the services such that these functions are processed in the order defined in the corresponding SFC, the end-to-end (E2E) latency constraints of all services are guaranteed, and all cloud and communication resource budget constraints are respected. In this paper, we first propose a new mixed binary linear program (MBLP) formulation of the above network slicing problem that optimizes the system energy efficiency while jointly considers the E2E latency requirement, resource budget, flow routing, and functional instantiation. Then, we develop another MBLP formulation and show that the two formulations are equivalent in the sense that they share the same optimal solution. However, since the numbers of variables and constraints in the second problem formulation are significantly smaller than those in the first one, solving the second problem formulation is more computationally efficient especially when the dimension of the corresponding network is large. Numerical results demonstrate the advantage of the proposed formulations compared with the existing ones. Copyright © 2020, The Authors. All rights reserved.

关键词： Network function virtualization

来源：评论

学校读者我要写书评

暂无评论

Shape correspondence using anisotropic Chebyshev spectral CNNs

Shape correspondence using anisotropic Chebyshev spectral CN...

引用

Conference on Computer Vision and Pattern Recognition (CVPR)

作者： Qinsong Li Shengjun Liu Ling Hu Xinru Liu Institute of Engineering Modeling and Scientific Computing Central South University State Key Laboratory of High Performance Manufacturing Complex Central South University School of Mathematics and Computational Science Hunan First Normal University

ISBN: (数字)9781728171685

ISBN: (纸本)9781728171692

Establishing correspondence between shapes is a very important and active research topic in many domains. Due to the powerful ability of deep learning on geometric data, lots of attractive results have been achieved by convolutional neural networks (CNNs). In this paper, we propose a novel architecture for shape correspondence, termed Anisotropic Chebyshev spectral CNNs (ACSCNNs), based on a new extension of the manifold convolution operator. The extended convolution operators aggregate the local features of signals by a set of oriented kernels around each point, which allows to much more comprehensively capture the intrinsic signal information. Rather than using fixed oriented kernels in the spatial domain in previous CNNs, in our framework, the kernels are learned by spectral filtering, based on the eigen-decompositions of multiple Anisotropic Laplace-Beltrami Operators. To reduce the computational complexity, we employ an explicit expansion of the Chebyshev polynomial basis to represent the spectral filters whose expansion coefficients are trainable. Through the benchmark experiments of shape correspondence, our architecture is demonstrated to be efficient and be able to provide better than the state-of-the-art results in several datasets even if using constant functions as inputs.

关键词： Shape Manifolds Convolution Kernel Machine learning Eigenvalues and eigenfunctions Chebyshev approximation

来源：评论

学校读者我要写书评

暂无评论

A simple low-degree optimal finite element scheme for the elastic transmission eigenvalue problem

arXiv

引用

arXiv 2021年

作者： Xi, Yingxia Ji, Xia Zhang, Shuo School of Science Nanjing University of Science and Technology Nanjing210094 China School of Mathematics and Statistics Beijing Institute of Technology Beijing100081 China Beijing Key Laboratory on MCAACI Beijing Institute of Technology Beijing100081 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China

The paper presents a finite element scheme for the elastic transmission eigenvalue problem written as a fourth order eigenvalue problem. The scheme uses piecewise cubic polynomials and obtains optimal convergence rate. Compared with other low-degree and nonconforming finite element schemes, the scheme inherits the continuous bilinear form which does not need extra stabilizations and is thus simple to *** Codes 31A30, 65N30, 47B07 Copyright © 2021, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

来源：评论

学校读者我要写书评

暂无评论

A diffuse-interface lattice Boltzmann method for thermal particulate flows with Dirichlet boundary conditions

引用

Physics of Fluids 2025年第6期37卷

作者： Liu, Jiao Liu, Xi Chai, Zhenhua School of Mathematics and Computer Science Nanchang University Jiangxi Nanchang330031 China School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China The State Key Laboratory of Intelligent Manufacturing Equipment and Technology Huazhong University of Science and Technology Wuhan430074 China

The lattice Boltzmann method has been widely used to study thermal particulate flows that are usually observed in both nature and engineering, while how to efficiently and accurately treat the fluid-solid boundary conditions is still an important and not well-resolved issue. In this paper, a diffuse-interface lattice Boltzmann method (DI-LBM) is developed for complex thermal particulate flows with Dirichlet boundary conditions. Unlike the previous works where the fluid-solid boundary is treated as a sharp interface, the fluid-solid boundary in the DI-LBM is implemented as a diffuse interface such that the physical variables and transport coefficients in the fluid and solid regions are varied smoothly. To depict the diffuse interface, a smooth function is introduced, and simultaneously, an additional source term is added in the evolution equation to reflect the effect of Dirichlet boundary condition imposed on the fluid-solid boundary. The present method is also tested by several classical problems, and the numerical results show that the DI-LBM is not only of second-order convergence rate in space, but also efficient in the study of complex thermal particulate flows. © 2025 Author(s).

关键词： Kinetic theory of gases

来源：评论

学校读者我要写书评

暂无评论

Sentence segmentation for classical Chinese based on LSTM with radical embedding

引用

The Journal of China Universities of Posts and Telecommunications 2019年第2期26卷 1-8页

作者： Han Xu Wang Hongsu Zhang Sanqian Fu Qunchao Liu Jun School of software Engineering Beijing University of Posts and TelecommunicationsBeijing 100876China Key Laboratory of Trustworthy Distributed Computing and Service (BUPT)Ministry of EducationBeijing 100876China The Key Laboratory of Rich-Media Knowledge Organization and Service of Digital Publishing Content Institute of Scientific and Technical Information of ChinaBeijing 100038China Insitute of Quantitative Social Science Harvard UniversityCambridgeMAUSA Department of statistics Harvard UniversityCambridgeMAUSA

A low-than character feature embedding called radical embedding is proposed,and applied on a long-short term memory(LSTM) model for sentence segmentation of pre-modern Chinese *** dataset includes over 150 classical Chinese books from 3 different dynasties and contains different literary ***-conditional random fields(LSTM-CRF) model is a state-of-the-art method for the sequence labeling *** model adds a component of radical embedding,which leads to improved *** results based on the aforementioned Chinese books demonstrate better accuracy than earlier methods on sentence segmentation,especial in Tang’s epitaph texts(achieving an F1-score of 81.34%).

关键词： LSTM radical embedding sentence segmentation

来源：评论

学校读者我要写书评

暂无评论

SNIG PROPERTY OF MATRIX LOW-RANK FACTORIZATION MODEL

引用

Journal of Computational Mathematics 2018年第3期36卷 374-390页

作者： Hong Wang Xin Liu Xiaojun Chen Yaxiang Yuan Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

Recently, the matrix factorization model attracts increasing attentions in handling large-scale rank minimization problems, which is essentially a nonconvex minimization problem. Specifically, it is a quadratic least squares problem and consequently a quartic polynomial optimization problem. In this paper, we introduce a concept of the SNIG （＂Second-order Necessary optimality Implies Global optimality＂） condition which stands for the property that any second-order stationary point of the matrix factorization model must be a global minimizer. Some scenarios under which the SNIG condition holds are presented. Furthermore, we illustrate by an example when the SNIG condition may fail.

关键词： Low rank factorization Nonconvex optimization Second-order optimality condition Global minimizer

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：