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A Barzilai-Borwein conjugate gradient method

Science China mathematics 2016年第8期59卷 1511-1524页

作者： DAI YuHong KOU CaiXia LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems Science Chinese Academy of Sciences School of Science Beijing University of Posts and Telecommunications

The linear conjugate gradient method is an optimal method for convex quadratic minimization due to the Krylov subspace minimization property. The proposition of limited-memory BFGS method and Barzilai-Borwein gradient method, however, heavily restricted the use of conjugate gradient method for largescale nonlinear optimization. This is, to the great extent, due to the requirement of a relatively exact line search at each iteration and the loss of conjugacy property of the search directions in various occasions. On the contrary, the limited-memory BFGS method and the Barzilai-Bowein gradient method share the so-called asymptotical one stepsize per line-search property, namely, the trial stepsize in the method will asymptotically be accepted by the line search when the iteration is close to the solution. This paper will focus on the analysis of the subspace minimization conjugate gradient method by Yuan and Stoer(1995). Specifically, if choosing the parameter in the method by combining the Barzilai-Borwein idea, we will be able to provide some efficient Barzilai-Borwein conjugate gradient(BBCG) methods. The initial numerical experiments show that one of the variants, BBCG3, is specially efficient among many others without line searches. This variant of the BBCG method might enjoy the asymptotical one stepsize per line-search property and become a strong candidate for large-scale nonlinear optimization.

关键词： conjugate gradient method subspace minimization Barzilai-Bowein gradient method line search descent property global convergence

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MINIMAL CONSISTENT FINITE ELEMENT SPACE FOR THE BIHARMONIC EQUATION ON QUADRILATERAL GRIDS

arXiv

引用

arXiv 2017年

作者： Zhang, Shuo LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China

In this paper, a finite element space is presented on quadrilateral grids which can provide consistent discretization for the biharmonic equations. The space consists of piecewise quadratic polynomials and is of minim...

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A multi-level mixed element scheme of the two dimensional Helmholtz transmission eigenvalue problem

arXiv

引用

arXiv 2017年

作者： Xi, Yingxia Ji, Xia Zhang, Shuo LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China

In this paper, we present a multi-level mixed element scheme for the Helmholtz transmission eigenvalue problem on polygonal domains that are not necessarily able to be covered by rectangle grids. We first construct an equivalent linear mixed formulation of the transmission eigenvalue problem and then discretize it with Lagrangian finite elements of low regularities. The proposed scheme admits a natural nested discretization, based on which we construct a multi-level scheme. Optimal convergence rate and optimal computational cost can be obtained with the scheme.65N25, 65N30, 47B07 Copyright © 2017, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

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Stable mixed element schemes for plate models on multiply-connected domains

arXiv

引用

arXiv 2017年

作者： Zhang, Shuo LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China

In this paper, we study the mixed element schemes of the Reissner-Mindlin plate model and the Kirchhoff plate model in multiply-connected domains. By a regular decomposition of H0(rot, Ω) and a Helmholtz decomposition of its dual, we develop mixed formulations of the models which are equivalent to the primal ones respectively and which are uniformly stable. A framework of designing uniformly stable finite element schemes is presented, and a specific example is given. Copyright © 2017, The Authors. All rights reserved.

关键词： Finite element method

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Performance Prediction Based on Statistics of Sparse Matrix-Vector Multiplication on GPUs

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Journal of Computer and Communications 2017年第6期5卷 65-83页

作者： Ruixing Wang Tongxiang Gu Ming Li Country Graduate School of Chinese Academy of Engineering Physics Beijing China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing China Country Xi’an Aeronautics Computing Technique Research Institute AVIC Xi’an China

As one of the most essential and important operations in linear algebra, the performance prediction of sparse matrix-vector multiplication (SpMV) on GPUs has got more and more attention in recent years. In 2012, Guo and Wang put forward a new idea to predict the performance of SpMV on GPUs. However, they didn’t consider the matrix structure completely, so the execution time predicted by their model tends to be inaccurate for general sparse matrix. To address this problem, we proposed two new similar models, which take into account the structure of the matrices and make the performance prediction model more accurate. In addition, we predict the execution time of SpMV for CSR-V, CSR-S, ELL and JAD sparse matrix storage formats by the new models on the CUDA platform. Our experimental results show that the accuracy of prediction by our models is 1.69 times better than Guo and Wang’s model on average for most general matrices.

关键词： Sparse Matrix-Vector Multiplication Performance Prediction GPU Normal Distribution Uniform Distribution

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Securely outsourcing decentralized multi-authority attribute based signature 1

引用

9th International Symposium on Cyberspace Safety and Security, CSS 2017

作者： Sun, Jiameng Qin, Jing Ma, Jixin School of Mathematics Shandong University Jinan China State Key Laboratory of Information Security Institute of Information Engineering Chinese Academy of Sciences Beijing100093 China School of Computing and Mathematical Sciences Centre for Computer and Computational Science University of Greenwich London United Kingdom

ISBN: (数字)9783319694719

ISBN: (纸本)9783319694702

Attribute based signature (ABS) is a novel primitive of digital signature that allows the signer to endorse a piece of message with a set of certain attributes in order to preserve the privacy of the signer’s identity. There are multiple authorities that issue different secret keys for signer’s various attributes. And a central authority is usually established to manage all these attribute authorities. This brings a huge workload to compute a signature and also a threat to security and privacy if the central authority is compromised. In this paper, we present an outsourced decentralized multi-authority attribute based signature (ODMA-ABS) scheme. Compared with existing multi-authority attribute based signature schemes, the ODMA-ABS scheme achieves a stronger notion of attribute privacy and authority collusion resistance. And the workload to compute a signature is further reduced by utilizing the outsourcing technique, which makes our scheme more practical in reality. © 2017, Springer International Publishing AG.

关键词： Outsourcing

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An Efficient Inexact Newton-CG Algorithm for the Smallest Enclosing Ball Problem of Large Dimensions

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Journal of the Operations Research Society of China 2016年第2期4卷 167-191页

作者： Ya-Feng Liu Rui Diao Feng Ye Hong-Wei Liu State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Department of Applied Mathematics Xidian UniversityXi’an 710071China

In this paper,we consider the problem of computing the smallest enclosing ball(SEB)of a set of m balls in Rn,where the product mn is *** first approximate the non-differentiable SEB problem by its log-exponential aggregation function and then propose a computationally efficient inexact Newton-CG algorithm for the smoothing approximation problem by exploiting its special(approximate)sparsity *** key difference between the proposed inexact Newton-CG algorithm and the classical Newton-CG algorithm is that the gradient and the Hessian-vector product are inexactly computed in the proposed algorithm,which makes it capable of solving the large-scale SEB *** give an adaptive criterion of inexactly computing the gradient/Hessian and establish global convergence of the proposed *** illustrate the efficiency of the proposed algorithm by using the classical Newton-CG algorithm as well as the algorithm from Zhou et al.(Comput Optim Appl 30:147–160,2005)as benchmarks.

关键词： Smallest enclosing ball Smoothing approximation Inexact gradient Inexact Newton-CG algorithm Global convergence

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Large Shape Staggering in Neutron-Deficient Bi Isotopes

引用

Physical Review Letters 2021年第19期127卷 192501-192501页

作者： A. Barzakh A. N. Andreyev C. Raison J. G. Cubiss P. Van Duppen S. Péru S. Hilaire S. Goriely B. Andel S. Antalic M. Al Monthery J. C. Berengut J. Bieroń M. L. Bissell A. Borschevsky K. Chrysalidis T. E. Cocolios T. Day Goodacre J.-P. Dognon M. Elantkowska E. Eliav G. J. Farooq-Smith D. V. Fedorov V. N. Fedosseev L. P. Gaffney R. F. Garcia Ruiz M. Godefroid C. Granados R. D. Harding R. Heinke M. Huyse J. Karls P. Larmonier J. G. Li (李冀光) K. M. Lynch D. E. Maison B. A. Marsh P. Molkanov P. Mosat A. V. Oleynichenko V. Panteleev P. Pyykkö M. L. Reitsma K. Rezynkina R. E. Rossel S. Rothe J. Ruczkowski S. Schiffmann C. Seiffert M. D. Seliverstov S. Sels L. V. Skripnikov M. Stryjczyk D. Studer M. Verlinde S. Wilman A. V. Zaitsevskii Petersburg Nuclear Physics Institute NRC Kurchatov Institute 188300 Gatchina Russia Department of Physics University of York York YO10 5DD United Kingdom Advanced Science Research Center Japan Atomic Energy Agency Tokai-mura Ibaraki 319-1195 Japan KU Leuven Instituut voor Kern- en Stralingsfysica B-3001 Leuven Belgium Université Paris-Saclay CEA LMCE 91680 Bruyères-le-Châtel France Institut d’Astronomie et d’Astrophysique CP-226 Université Libre de Bruxelles 1050 Brussels Belgium Department of Nuclear Physics and Biophysics Comenius University in Bratislava 84248 Bratislava Slovakia School of Physics University of New South Wales Sydney NSW 2052 Australia Instytut Fizyki Teoretycznej Uniwersytet Jagielloński ul. prof. Stanisława Łojasiewicza 11 Kraków Poland School of Physics and Astronomy The University of Manchester Manchester M13 9PL United Kingdom Van Swinderen Institute University of Groningen 9747 Groningen Netherlands CERN Esplanade des Particules 1 1211 Geneva 23 Switzerland Institut für Physik Johannes Gutenberg-Universität Mainz D-55128 Mainz Germany TRIUMF 4004 Wesbrook Mall Vancouver British Columbia V6T 2A3 Canada NIMBE CEA CNRS Universiteé Paris-Saclay CEA Saclay 91190 Gif-sur-Yvette France Poznan University of Technology Piotrowo 3 Poznan 60-965 Poland School of Chemistry Tel Aviv University 69978 Tel Aviv Israel School of Engineering and Computing University of the West of Scotland Paisley PA1 2BE United Kingdom SQUARES CP160/09 Université libre de Bruxelles Av. F.D. Roosevelt 50 1050 Brussels Belgium Department of Physics University of Gothenburg SE-412 96 Gothenburg Sweden Institute of Applied Physics and Computational Mathematics Beijing 100088 China Saint Petersburg State University 7/9 Universitetskaya nab. St. Petersburg 199034 Russia Department of Chemistry M. V. Lomonosov Moscow State University Leninskie gory 1/3 Moscow 119991 Russia Department of Chemistry University of Helsinki P.O. Box 55 (A. I. Virtasen a

The changes in the mean-square charge radius (relative to Bi209), magnetic dipole, and electric quadrupole moments of Bi187,188,189,191 were measured using the in-source resonance-ionization spectroscopy technique at ISOLDE (CERN). A large staggering in radii was found in Bi187,188,189g, manifested by a sharp radius increase for the ground state of Bi188 relative to the neighboring Bi187,189g. A large isomer shift was also observed for Bi188m. Both effects happen at the same neutron number, N=105, where the shape staggering and a similar isomer shift were observed in the mercury isotopes. Experimental results are reproduced by mean-field calculations where the ground or isomeric states were identified by the blocked quasiparticle configuration compatible with the observed spin, parity, and magnetic moment.

关键词： Nuclear charge distribution Nuclear density functional theory Nuclear spin & parity Nuclear structure & decays Spectroscopic factors & electromagnetic moments

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A confidentiality preserving publicly verifiable computation for multivariate polynomials 15

A confidentiality preserving publicly verifiable computation...

引用

15th IEEE/ACIS International Conference on Software engineering Research, Management and Applications, SERA 2017

作者： Jiameng, Sun Binrui, Zhu Jing, Qin Jixin, Ma School of Mathematics Shandong University Jinan250100 China State Key Laboratory of Information Security Institute of Information Engineering Chinese Academy of Sciences Beijing100093 China Centre for Computer and Computational Science School of Computing and Mathematical Sciences University of Greenwich London United Kingdom

ISBN: (纸本)9781509057566

With the development of cloud services, outsourcing computation tasks to a commercial cloud server has drawn attentions by various communities, especially in the Big Data age. Public verifiability offers a flexible functionality in real circumstance where the cloud service provider (CSP) may be untrusted or some malicious users may slander the CSP on purpose. However, sometimes the computational result is sensitive and is not willing to be exposed in the public verification phase. In this paper, we present a confidential-preserving public verifiable computation (CP-PVC) scheme for Evaluation of High Degree Polynomials. Compared with previous proposals, our scheme achieves confidentiality of computational result, while not sacrificing the property of public verifiability. We also provide the algorithm and experimental evaluation to show the efficiency of our scheme. © 2017 IEEE.

关键词： Polynomials

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Anisotropic adaptive finite element method for magnetohydrodynamic flow at high Hartmann numbers

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Applied mathematics and Mechanics(English Edition) 2016年第11期37卷 1479-1500页

作者： Jikun ZHAO Shipeng MAO Weiying ZHENG School of Mathematics and Statistics Zhengzhou University State Key Laboratory of Scientific and Engineering Computing (LSEC) and Institute of Computational Mathematics Academy of Mathematics and Systems Science (AMSS) Chinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences

This paper presents an anisotropic adaptive finite element method （FEM） to solve the governing equations of steady magnetohydrodynamic （MHD） duct flow. A resid- ual error estimator is presented for the standard FEM, and two-sided bounds on the error independent of the aspect ratio of meshes are provided. Based on the Zienkiewicz-Zhu es- timates, a computable anisotropic error indicator and an implement anisotropic adaptive refinement for the MHD problem are derived at different values of the Hartmann number. The most distinguishing feature of the method is that the layer information from some directions is captured well such that the number of mesh vertices is dramatically reduced for a given level of accuracy. Thus, this approach is more suitable for approximating the layer problem at high Hartmann numbers. Numerical results show efficiency of the algorithm.

关键词： magnetohydrodynamic （MHD） flow posteriori error estimate anisotropicadaptive finite element method （FEM）

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