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A Parallel Line Search Subspace Correction Method for Composite Convex Optimization

Journal of the Operations Research Society of China 2015年第2期3卷 163-187页

作者： Qian Dong Xin Liu Zai-Wen Wen Ya-Xiang Yuan State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina Beijing International Center for Mathematical Research Peking UniversityBeijingChina

In this paper,we investigate a parallel subspace correction framework for composite convex *** variables are first divided into a few blocks based on certain *** each iteration,the algorithms solve a suitable subproblem on each block simultaneously,construct a search direction by combining their solutions on all blocks,then identify a new point along this direction using a step size satisfying the Armijo line search *** are called PSCLN and PSCLO,respectively,depending on whether there are overlapping regions between two imme-diately adjacent blocks of *** convergence is established under mild *** compare PSCLN and PSCLO with the parallel version of the fast iterative thresholding algorithm and the fixed-point continuation method using the Barzilai-Borwein step size and the greedy coordinate block descent method for solving the l1-regularized minimization *** numerical results showthatPSCLN andPSCLOcan run fast and return solutions notworse than those from the state-of-theart algorithms on most test *** is also observed that the overlapping domain decomposition scheme is helpful when the data of the problem has certain special structures.

关键词： Line search Block coordinate descent method Domain decomposition Jacobian-type iteration Distributed optimization

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Multiscale method for identifying and marking the multiform fractures from visible-light rock-mass images

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Underground Space 2024年第3期16卷 279-300页

作者： Yongbo Pan Junzhi Cui Zhenhao Xu School of Mathematics and Statistics Zhengzhou UniversityZhengzhou 450001China The State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China Geotechnical and Structural Engineering Research Center Shandong UniversityJinan 250100China

Multiform fractures have a direct impact on the mechanical performance of rock *** accurately identify multiform fractures,the distribution patterns of grayscale and the differential features of fractures in their neighborhoods are *** on this,a multiscale processing algorithm is *** multiscale process is as *** the neighborhood of pixels,a grayscale continuous function is constructed using bilinear interpolation,the smoothing of the grayscale function is realized by Gaussian local filtering,and the grayscale gradient and Hessian matrix are calculated with high *** small-scale blocks,the pixels are classified by adaptively setting the grayscale threshold to identify potential line segments and *** the global image,potential line segments and mini-fillings are spliced together by progressing the block frontier layer-by-layer to identify and mark multiform *** accuracy of identifying multiform fractures is improved by constructing a grayscale continuous function and adaptively setting the grayscale thresholds on small-scale *** the layer-by-layer splicing algorithm is performed only on the domain of the 2-layer small-scale blocks,reducing the *** using rock mass images with different fracture types as examples,the identification results show that the proposed algorithm can accurately identify the multiform fractures,which lays the foundation for calculating the mechanical parameters of rock masses.

关键词： Visible light rock-mass images Continuous grayscale function Small-scale blocks Multiform fractures

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Interaction Between Line Soliton and Algebraic Soliton for Asymmetric Nizhnik-Novikov-Veselov Equation

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Communications in Theoretical Physics 2008年第6期49卷 1547-1552页

作者： RUAN Hang-Yu LI Zhi-Fang Department of Physics Ningbo University Ningbo 315211 China Nonlinear Science Center and Physics Department Ningbo University Ningbo 315211 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and System Sciences the Chinese Academy of Sciences P.O. Box 2719 Beijing 100080 China

Starting from the variable separation approach, the algebraic soliton solution and the solution describing the interaction between line soliton and algebraic soliton are obtained by selecting appropriate seed solution for （2＋1）-dimensional ANNV equation. The behaviors of interactions are discussed in detail both analytically and graphically. It is shown that there are two kinds of singular interactions between line soliton and algebraic soliton： 1） the resonant interaction where the algebraic soliton propagates together with the line soliton and persists infinitely; 2） the extremely repulsive interaction where the algebraic soliton affects the motion of the line soliton infinitely apart.

关键词： variable separation approach the interaction between line soliton and algebraic soliton （2＋1）-dimensional ANNV equation

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On Minimization of Upper Bound for the Convergence Rate of the QHSS Iteration Method

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Communications on Applied Mathematics and Computation 2019年第2期1卷 263-282页

作者： Wen-Ting Wu State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of Sciences. P.O. Box 2719. Beijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

For an upper bound of the spectral radius of the QHSS (quasi Hermitian and skew-Hermitian splitting) iteration matrix which can also bound the contraction factor of the QHSS iteration method,we give its minimum point under the conditions which guarantee that the upper bound is strictly less than one. This provides a good choice of the involved iteration parameters,so that the convergence rate of the QHSS iteration method can be significantly improved.

关键词： System of linear equations Non-Hermitian matrix QHSS iteration method Convergence rate

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Conformal Invariant Asymptotic Expansion Approach for Solving （3＋1）-Dimensional JM Equation

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Communications in Theoretical Physics 2006年第6期45卷 979-984页

作者： LI Zhi-Fang RUAN Hang-Yu Department of Physics Ningbo University Ningbo 315211 China Nonlinear Science Center and Physics Department Ningbo University Ningbo 315211 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and System Sciences the Chinese Academy of Sciences P.O. Box 2719 Beijing 100080 China

The （3＋1）-dimensional Jimbo-Miwa （JM） equation is solved approximately by using the conformal invariant asymptotic expansion approach presented by Ruan. By solving the new （3＋1）-dimensional integrable models, which are conformal invariant and possess Painlevé property, the approximate solutions are obtained for the JM equation, containing not only one-soliton solutions but also periodic solutions and multi-soliton solutions. Some approximate solutions happen to be exact and some approximate solutions can become exact by choosing relations between the parameters properly.

关键词：（3＋1）-dimensional Jimbo-Miwa （JM） equation conformal invariant asymptotic expansion approach Painlevé property approximate and exact solutions

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Integrable couplings of a generalized AKNS hierarchy

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Journal of Central South University of Technology 2002年第3期9卷 220-223页

作者：张玉峰张鸿庆闫庆友 State Key Laboratory of Scientific and Engineering Computing Academia Sinica Beijing 100080 China School of Information Shandong University of Science and Technology Taian 271019 China

A generalized AKNS isospectral problem where the trace of corresponding spectral matrix is not zero, is transformed to a new isospectral problem where the trace of the resulting matrix is zero, by using transformation of Lax pairs, and these two spectral problems lead to the same hierarchy of equations. The authors started from the transformed spectral problem and constructed a new loop algebra which has not appeared before, and obtained the integrable coupling of the generalized AKNS hierarchy. Specially, the integrable couplings of the KdV equation and MKdV equation are obtained.

关键词： integrable coupling AKNS hierarchy spectral problem

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Pseudo complementary measurement for traditional single-pixel cameras

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Chinese Physics B 2020年第11期29卷 315-322页

作者： Qian Dong Xu-Ri Yao Xin Liu Bing Liu Guang-Jie Zhai State Key Laboratory of Computer Science Institute of SoftwareChinese Academy of SciencesBeijing 100190China Key Laboratory of Electronics and Information Technology for Space Systems National Space Science CenterChinese Academy of SciencesBeijing 100190China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100049China

A traditional single-pixel camera needs a large number of measurements to reconstruct the object with compressive sensing *** with the 1/0 matrices in classical measurement,the 1/-1 matrices in the complementary measurement has better property for reconstruction computation and returns better reconstruction ***,each row of the 1/-1 matrices needs two measurements with the traditional single-pixel camera which results into double measurements compared with the 1/0 *** this paper,we consider the pseudo complementary measurement which only takes the same amount of measurements with the row number of some properly designed 1/0 matrix to compute the total luminous flux of the objective and derives the measurement data of the corresponding 1/-1 matrix in a mathematical *** numerical simulation and experimental result show that the pseudo complementary measurement is an efficient tool for the traditional single-pixel camera imaging under low measurement rate,which can combine the advantages of the classical and complementary measurements and significantly improve the peak signal-to-noise ratio.

关键词： computational imaging single-pixel camera

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A New Sixth-Order WENO Scheme for Solving Hyperbolic Conservation Laws

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Communications on Applied Mathematics and Computation 2023年第1期5卷 3-30页

作者： Kunlei Zhao Yulong Du Li Yuan State Key Laboratory of Scientific and Engineering Computing(LSEC)and Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100190China School of Mathematical Sciences Beihang UniversityBeijing 100191China

In this paper,we develop a new sixth-order WENO scheme by adopting a convex combina-tion of a sixth-order global reconstruction and four low-order local *** the classical WENO schemes,the associated linear weights of the new scheme can be any positive numbers with the only requirement that their sum equals ***,a very simple smoothness indicator for the global stencil is *** new scheme can achieve sixth-order accuracy in smooth *** tests in some one-and two-dimensional bench-mark problems show that the new scheme has a little bit higher resolution compared with the recently developed sixth-order WENO-Z6 scheme,and it is more efficient than the classical fifth-order WENO-JS5 scheme and the recently developed sixth-order WENO6-S scheme.

关键词： Global smoothness indicator Linear weights Sixth-order accuracy WENO

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Flexible alignment of images using B-spline reparameterization based on multi-resolution representations - Computational methods

Flexible alignment of images using B-spline reparameterizati...

引用

International Conference on Intelligent Computation Technology and Automation

作者： Zheng, Yanmei Xu, Guoliang State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics Academy of Mathematics and System Sciences Beijing 100190 China

ISBN: (纸本)9780769543536

We present a new flexible alignment method to align two or more similar images, especially biological images. By minimizing an energy functional measuring the difference of the initial image and target image, an L2-gradient flow is derived. The flow is integrated by a finite element method in the spatial direction and an explicit Euler scheme in the temporal direction. Multi-resolution representations are used for achieving efficient multi-scale alignment. The experimental results on 2D images show that the proposed method is efficient, effective, robust and capable of capturing the variation of the initial and target images, from large to small scale. © 2011 IEEE.

关键词： Finite element method

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Infinitely Many Symmetries of Konopelchenko-Dubrovsky Equation

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Communications in Theoretical Physics 2005年第3X期44卷 385-388页

作者： LI Zhi-Fang RUAN Hang-Yu Department of Physics Ningbo University Ningbo 315211 China Nonlinear Science Center and Physics Department of Ningbo University Ningbo 315211 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and System Sciences the Chinese Academy of Sciences P.O. Box 2719 Beijing 100080 China

A set of generalized symmetries with arbitrary functions of t for the Konopelchenko-Dubrovsky (KD)equation in 2+1 space dimensions is given by using a direct method called formal function series method presented by Lo... 详细信息

关键词： formal function series method Konopelchenko-Dubrovsky equation infinite dimensional generalized ω∞ algebra

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