检索结果-内蒙古大学图书馆

ERROR ANALYSIS OF FRACTIONAL COLLOCATION METHODS FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH NONCOMPACT OPERATORS

引用

Journal of Computational Mathematics 2025年第3期43卷 690-707页

作者： Zheng Ma Chengming Huang Anatoly A.Alikhanov School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China North-Caucasus Center for Mathematical Research North-Caucasus Federal UniversityStavropol 355017Russia North-Eastern Federal University Yakutsk 677000Russia

This paper is concerned with the numerical solution of Volterra integro-differential equations with noncompact *** focus is on the problems with weakly singular *** handle the initial weak singularity of the solution,a fractional collocation method is applied.A rigorous hp-version error analysis of the numerical method under a weighted H1-norm is carried *** result shows that the method can achieve high order convergence for such *** experiments are also presented to confirm the effectiveness of the proposed method.

关键词： Volterra integro-differential equation Noncompact operator Nonsmooth solution Collocation method Fractional polynomial hp-version error analysis

来源：评论

学校读者我要写书评

暂无评论

Model-based Visual 3D Pose Tracking of Non-cooperative Spacecraft in Close Range 74

Model-based Visual 3D Pose Tracking of Non-cooperative Space...

引用

74th International Astronautical Congress, IAC 2023

作者： Liu, Chang Tang, Hao Shenzhen Institutes of Advanced Technology Chinese Academy of Sciences Guangdong Shenzhen518055 China Shenzhen Key Laboratory for Exascale Engineering and Scientific Computing Shenzhen China

This work proposes a new monocular algorithm to track the 3D pose of non-cooperative spacecraft for proximity operations in real time with the 3D boundaries and 3D contour of the spacecraft as features. The 3D boundary segments of the spacecraft are automatically extracted from the 3D spacecraft model a priori. At the beginning instant of tracking, the tracking system is initialized by a pose retrieval method. At the following time instant, with the initial pose and its covariance provided by the extended Kalman filter (EKF), the 3D contour segments are rapidly extracted from the 3D model. The boundary segments and contour segments are taken as 3D features. In the input image, we search the image data corresponding to the 3D features within the range decided by the initial pose and its covariance. Then, the spacecraft pose is determined in real time by minimizing the geometric distances of the 3D features to the back-projection lines of their corresponding image data. The covariance of the pose is estimated via the first-order optimal condition of the minimization. Eventually, the EKF is derived from the second-order autoregression (2nd-AR) to generate the final pose estimate, and the initial pose and its covariance for next time instant. The synthetic trials quantitatively indicate that our method can track the 3D pose of spacecraft in real time with high accuracy and has outstanding robustness to the dark occlusion, cluster background, large image distance, and image noise. The real trial qualitatively validates the effectiveness of our tracking method. Copyright © 2023 by the International Astronautical Federation (IAF). All rights reserved.

关键词： Kalman filter Pose determination Spacecraft Tracking

来源：评论

学校读者我要写书评

暂无评论

A NEW ADAPTIVE SUBSPACE MINIMIZATION THREE-TERM CONJUGATE GRADIENT ALGORITHM FOR UNCONSTRAINED OPTIMIZATION

引用

Journal of Computational Mathematics 2021年第2期39卷 159-177页

作者： Keke Zhang Hongwei Liu Zexian Liu School of Mathematics and Statistics Xidian UniversityXi’an 710126China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering computingAMSSChinese Academy of SciencesBeijing 100190China

A new adaptive subspace minimization three-term conjugate gradient algorithm with nonmonotone line search is introduced and analyzed in this *** search directions are computed by minimizing a quadratic approximation of the objective function on special subspaces,and we also proposed an adaptive rule for choosing different searching directions at each *** obtain a significant conclusion that the each choice of the search directions satisfies the sufficient descent *** the used nonmonotone line search,we prove that the new algorithm is globally convergent for general nonlinear functions under some mild *** experiments show that the proposed algorithm is promising for the given test problem set.

关键词： Conjugate gradient method Nonmonotone line search Subspace minimization Sufficient descent condition Global convergence

来源：评论

学校读者我要写书评

暂无评论

Convergence of Physics-Informed Neural Networks Applied to Linear Second-Order Elliptic Interface Problems

引用

Communications in Computational Physics 2023年第2期33卷 596-627页

作者： Sidi Wu Aiqing Zhu Yifa Tang Benzhuo Lu State Key Laboratory of Scientific and Engineering Computing National Center for Mathematics and Interdisciplinary SciencesAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China.

With the remarkable empirical success of neural networks across diverse scientific disciplines,rigorous error and convergence analysis are also being developed and ***,there has been little theoretical work focusing on neural networks in solving interface *** this paper,we perform a convergence analysis of physics-informed neural networks(PINNs)for solving second-order elliptic interface ***,we consider PINNs with domain decomposition technologies and introduce gradient-enhanced strategies on the interfaces to deal with boundary and interface jump *** is shown that the neural network sequence obtained by minimizing a Lipschitz regularized loss function converges to the unique solution to the interface problem in H2 as the number of samples *** experiments are provided to demonstrate our theoretical analysis.

关键词： Elliptic interface problems generalization errors convergence analysis neural networks.

来源：评论

学校读者我要写书评

暂无评论

Two-Stage Submodular Maximization Under Knapsack Problem

引用

Tsinghua Science and Technology 2024年第6期29卷 1703-1708页

作者： Zhicheng Liu Jing Jin Donglei Du Xiaoyan Zhang Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing 100124China College of Taizhou Nanjing Normal UniversityTaizhou 225300China Faculty of Management University of New BrunswickFrederictonE3B 5A3Canada School of Mathematical Science Institute of Mathematicsand Ministry of Education Key Laboratory of NSLSCSNanjing Normal UniversityNanjing 210023China

Two-stage submodular maximization problem under cardinality constraint has been widely studied in machine learning and combinatorial *** this paper,we consider knapsack *** this problem,we give n articles and m categories,and the goal is to select a subset of articles that can maximize the function F(S).Function F(S)consists of m monotone submodular functions fj,j=1,2,…,m,and each fj measures the similarity of each article in category *** present a constant-approximation algorithm for this problem.

关键词： submodular function knapsack constraint matroid

来源：评论

学校读者我要写书评

暂无评论

Phase-field-based lattice Boltzmann method for containerless freezing

引用

Physical Review E 2024年第3期110卷 035301页

作者： Jiangxu Huang Lei Wang Zhenhua Chai Baochang Shi School of Mathematics and Statistics School of Mathematics and Physics Institute of Interdisciplinary Research for Mathematics and Applied Science Hubei Key Laboratory of Engineering Modeling and Scientific Computing

In this paper we first propose a phase-field model for the containerless freezing problems, in which the volume expansion or shrinkage of the liquid caused by the density change during the phase change process is considered by adding a mass source term to the continuum equation. Then a phase-field-based lattice Boltzmann (LB) method is further developed to simulate solid-liquid phase change phenomena in multiphase systems. We test the developed LB method by the problem of conduction-induced freezing in a semi-infinite space, the three-phase Stefan problem, and the droplet solidification on a cold surface, and the numerical results are in agreement with the analytical and experimental solutions. In addition, the LB method is also used to study the rising bubbles with solidification. The results of the present method not only accurately capture the effect of bubbles on the solidification process, but also are in agreement with the previous work. Finally, a parametric study is carried out to examine the influences of some physical parameters on the sessile droplet solidification, and it is found that the time of droplet solidification increases with the increase of droplet volume and contact angle.

关键词： Drops & bubbles Liquid-solid phase transition

来源：评论

学校读者我要写书评

暂无评论

On eigenvalues of a high-dimensional Kendall's rank correlation matrix with dependence

引用

Science China Mathematics 2023年第11期66卷 2615-2640页

作者： Zeng Li Cheng Wang Qinwen Wang Department of Statistics and Data Science Southern University of Science and TechnologyShenzhen 518055China School of Mathematical Sciences Shanghai Jiao Tong UniversityShanghai 200240China Key Laboratory of Scientific and Engineering Computing(Shanghai Jiao Tong University) Shanghai 200240China School of Data Science Fudan UniversityShanghai 200433China

In this paper,we investigate the limiting spectral distribution of a high-dimensional Kendall’s rank correlation *** underlying population is allowed to have a general dependence *** result no longer follows the generalized Marcenko-Pastur law,which is brand *** is the first result on rank correlation matrices with *** applications,we study Kendall’s rank correlation matrix for multivariate normal distributions with a general covariance *** these results,we further gain insights into Kendall’s rank correlation matrix and its connections with the sample covariance/correlation matrix.

关键词： Hoeffding decomposition Kendall's rank correlation matrix limiting spectral distribution random matrix theory

来源：评论

学校读者我要写书评

暂无评论

REQUIRED NUMBER OF ITERATIONS FOR SPARSE SIGNAL RECOVERY VIA ORTHOGONAL LEAST SQUARES

引用

Journal of Computational Mathematics 2023年第1期41卷 1-17页

作者： Haifeng Li Jing Zhang Jinming Wen Dongfang Li Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control College of Mathematics and Information ScienceHenan Normal UniversityXinxiang 453007China College of Information Science and Technology Jinan UniversityGuangzhou 510632China School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China

In countless applications,we need to reconstruct a K-sparse signal x∈R n from noisy measurements y=Φx+v,whereΦ∈R^(m×n)is a sensing matrix and v∈R m is a noise *** least squares(OLS),which selects at each step the column that results in the most significant decrease in the residual power,is one of the most popular sparse recovery *** this paper,we investigate the number of iterations required for recovering x with the OLS *** show that OLS provides a stable reconstruction of all K-sparse signals x in[2.8K]iterations provided thatΦsatisfies the restricted isometry property(RIP).Our result provides a better recovery bound and fewer number of required iterations than those proposed by Foucart in 2013.

关键词： Sparse signal recovery Orthogonal least squares(OLS) Restricted isometry property(RIP)

来源：评论

学校读者我要写书评

暂无评论

A space-decoupling framework for optimization on bounded-rank matrices with orthogonally invariant constraints

arXiv

引用

arXiv 2025年

作者： Yang, Yan Gao, Bin Yuan, Ya-Xiang State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences The University of Chinese Academy of Sciences Beijing China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

Imposing additional constraints on low-rank optimization has garnered growing interest. However, the geometry of coupled constraints hampers the well-developed low-rank structure and makes the problem intricate. To this end, we propose a space-decoupling framework for optimization on bounded-rank matrices with orthogonally invariant constraints. The "space-decoupling" is reflected in several ways. We show that the tangent cone of coupled constraints is the intersection of tangent cones of each constraint. Moreover, we decouple the intertwined bounded-rank and orthogonally invariant constraints into two spaces, leading to optimization on a smooth manifold. Implementing Riemannian algorithms on this manifold is painless as long as the geometry of additional constraints is known. In addition, we unveil the equivalence between the reformulated problem and the original problem. Numerical experiments on real-world applications—spherical data fitting, graph similarity measuring, low-rank SDP, model reduction of Markov processes, reinforcement learning, and deep learning—validate the superiority of the proposed framework. Copyright © 2025, The Authors. All rights reserved.

关键词： Markov processes

来源：评论

学校读者我要写书评

暂无评论

DISCRETE ENERGY ANALYSIS OF THE THIRD-ORDER VARIABLE-STEP BDF TIME-STEPPING FOR DIFFUSION EQUATIONS

引用

Journal of Computational Mathematics 2023年第2期41卷 325-344页

作者： Hong-lin Liao Tao Tang Tao Zhou Department of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211106China Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA) MIITNanjing 211106China Division of Science and Technology BNU-HKBU United International CollegeZhuhai 519087China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing100190China

This is one of our series works on discrete energy analysis of the variable-step BDF *** this part,we present stability and convergence analysis of the third-order BDF(BDF3)schemes with variable steps for linear diffusion equations,see,e.g.,[SIAM ***.,58:2294-2314]and[***.,90:1207-1226]for our previous works on the BDF2 *** this aim,we first build up a discrete gradient structure of the variable-step BDF3 formula under the condition that the adjacent step ratios are less than 1.4877,by which we can establish a discrete energy dissipation ***-robust stability and convergence analysis in the L^(2) norm are then *** the mesh robustness means that the solution errors are well controlled by the maximum time-step size but independent of the adjacent time-step *** also present numerical tests to support our theoretical results.

关键词： Diffusion equations Variable-step third-order BDF scheme Discrete gradient structure Discrete orthogonal convolution kernels Stability and convergence

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：