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LOW RANK APPROXIMATION SOLUTION OF A CLASS OF GENERALIZED LYAPUNOV EQUATION

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Journal of computational Mathematics 2016年第4期34卷 407-420页

作者： Xuefeng Duan Zhuling Jiang Anping Liao College of Mathematics and Computational Science Guilin University of Electronic Technology Guilin 541004 P.R. China Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Teehnology Guilin 541004 P.R. China College of Mathematics and Econometrics Hunan University Changsha 410082 P.R. China

In this paper, we consider the low rank approximation solution of a generalized Lya- punov equation which arises in the bilinear model reduction. By using the variation prin- ciple, the low rank approximation solution problem is transformed into an unconstrained optimization problem, and then we use the nonlinear conjugate gradient method with ex- act line search to solve the equivalent unconstrained optimization problem. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed methods.

关键词： Generalized Lyapunov equation Bilinear model reduction Low rank approxi-mation solution Numerical method.

An efficient npn boolean matching algorithm based on structural signature and shannon expansion

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arXiv 2017年

作者： Zhang, Juling Yang, Guowu Hung, William N.N. Zhang, Yan Wu, Jinzhao Big Data Research Center School of Computer Science and Engineering University of Electronic Science and Technology of China Chengdu611731 China Synopsys Inc. Mountain ViewCA United States Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis Guangxi University for Nationalities Nanning530006 China

An efficient pairwise Boolean matching algorithm for solving the problem of matching single-output specified Boolean functions under input negation and/or input permutation and/or output negation (NPN) is proposed in this paper. We present the structural signature (SS) vector, which comprises a first-order signature value, two symmetry marks, and a group mark. As a necessary condition for NPN Boolean matching, the SS is more effective than the traditional signature. Two Boolean functions, f and g, may be equivalent when they have the same SS vector. A symmetry mark can distinguish symmetric variables and asymmetric variables and be used to search for multiple variable mappings in a single variable-mapping search operation, which reduces the search space significantly. Updating the SS vector via Shannon decomposition provides benefits in distinguishing unidentified variables, and the group mark and phase collision check can be used to discover incorrect variable mappings quickly, which also speeds up the NPN Boolean matching process. Using the algorithm proposed in this paper, we test both equivalent and non-equivalent matching speeds on the MCNC benchmark circuit sets and random circuit sets. In the experiment, our algorithm is shown to be 4.2 times faster than competitors when testing equivalent circuits and 172 times faster, on average, when testing non-equivalent circuits. The experimental results show that our approach is highly effective at solving the NPN Boolean matching problem. Copyright © 2017, The Authors. All rights reserved.

关键词： Mapping

A canonical-based NPN boolean matching algorithm utilizing boolean difference and cofactor signature

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arXiv 2017年

作者： Zhang, Juling Yang, Guowu Hung, W.N.N. Wu, Jinzhao Big Data Research Center School of Computer Science and Engineering University of Electronic Science and Technology of China Chengdu611731 China Synopsys Inc. Mountain ViewCA United States Guangxi Key Laboratory of Hybrid Computation IC Design Analysis Guangxi University for Nationalities Nanning530006 China

This paper presents a new compact canonical-based algorithm to solve the problem of single-output completely specified NPN Boolean matching. We propose a new signature vector Boolean difference and cofactor (DC) signature vector. Our algorithm utilizes the Boolean difference, cofactor signature and symmetry properties to search for canonical transformations. The use of symmetry and Boolean difference notably reduces the search space and speeds up the Boolean matching process compared to the algorithm proposed in [1]. We tested our algorithm on a large number of circuits. The experimental results showed that the average runtime of our algorithm 37% higher and its average search space 67% smaller compared to [1] when tested on general circuits. Copyright © 2017, The Authors. All rights reserved.

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A Two-grid Method for Linearizing and Symmetrizing the Steady-state Poisson-Nernst-Planck Equations

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arXiv 2017年

作者： Li, Xuefang Yang, Ying Cheng, Hang School of Mathematics and Computing Science Guilin University of Electronic Technology Guilin Guangxi541004 China School of Mathematics and Computing Science Guangxi Colleges Universities Key Laboratory of Data Analysis and Computation Guangxi Key Laboratory of Cryptography and information Security Guilin University of Electronic Technology Guilin Guangxi541004 China School of Mathematics and Computing Science Guilin University of Electronic Technology Guilin Guangxi541004 China

In this paper, a two-grid method is proposed to linearize and symmetrize the steady-state Poisson-Nernst-Planck equations. The computational system is decoupled to linearize and symmetrize equations by using this method, which can improve the computational efficiency compared with the finite element method. Error estimates are derived for the proposed method. The numerical results show that the two-grid method is effective.65N30, 92C40. Copyright © 2017, The Authors. All rights reserved.

关键词： Finite element method

Least-Squares Solutions of Generalized Sylvester Equation with Xi Satisfies Different Linear Constraint

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Advances in Linear Algebra & Matrix Theory 2016年第2期6卷 59-74页

作者： Xuelin Zhou Dandan Song Qingle Yang Jiaofen Li School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Technology Guilin China

In this paper, an iterative method is constructed to find the least-squares solutions of generalized Sylvester equation , where is real matrices group, and satisfies different linear constraint. By this iterative method, for any initial matrix group within a special constrained matrix set, a least squares solution group with satisfying different linear constraint can be obtained within finite iteration steps in the absence of round off errors, and the unique least norm least-squares solution can be obtained by choosing a special kind of initial matrix group. In addition, a minimization property of this iterative method is characterized. Finally, numerical experiments are reported to show the efficiency of the proposed method.

关键词： Least-Squares Problem Centro-Symmetric Matrix Bisymmetric Matrix Iterative Method

The weighted horizontal linear complementarity problem on a Euclidean Jordan algebra

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arXiv 2017年

作者： Chi, Xiaoni Gowda, M. Seetharama Tao, Jiyuan School of Mathematics and Computing Science Guangxi Colleges Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Technology Guilin Guangxi541004 China Department of Mathematics and Statistics University of Maryland Baltimore County BaltimoreMD 21250 United States Department of Mathematics and Statistics Loyola University Maryland BaltimoreMD21210 United States

A weighted complementarity problem (wCP) is to find a pair of vectors belonging to the intersection of a manifold and a cone such that the product of the vectors in a certain algebra equals a given weight vector. If the weight vector is zero, we get a complementarity problem. Examples of such problems include the Fisher market equilibrium problem and the linear programming and weighted centering problem. In this paper we consider the weighted horizontal linear complementarity problem (wHLCP) in the setting of Euclidean Jordan algebras and establish some existence and uniqueness results. For a pair of linear transformations on a Euclidean Jordan algebra, we introduce the concepts of R0, R, and P properties and discuss the solvability of wHCLPs under nonzero (topological) degree conditions. A uniqueness result is stated in the setting of Rn. We show how our results naturally lead to interior point *** Codes 90C30 Copyright © 2017, The Authors. All rights reserved.

关键词： Vectors

Single Peak Soliton and Periodic Cusp Wave of the Generalized Schrodinger-Boussinesq Equations

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Communications in Theoretical Physics 2015年第6期63卷 731-742页

作者：乔丽静唐生强赵海霞 School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationGuilin University of Electronic Technology

In this paper, we study peakon, cuspon, smooth soliton and periodic cusp wave of the generalized Schr6dinger-Boussinesq equations. Based on the method of dynamical systems, the generalized Schr6dinger-Boussinesq equations are shown to have new the parametric representations of peakon, cuspon, smooth solRon and periodic cusp wave solutions. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are g/van.

关键词： method of dynamical systems peakon cuspon periodic cusp wave generalized Schrodinger-Boussinesq equations

Variational inequality formulation of circular cone eigenvalue complementarity problems

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Fixed Point Theory and Applications 2016年第1期2016卷 1-14页

作者： Chi, Xiaoni Wei, Hongjin Feng, Yuqiang Chen, Jiawei School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Technology Guilin 541004 China Hubei Province Key Laboratory of Systems Science in Metallurgical Process Wuhan University of Science and Technology Wuhan 430081 China College of Science Wuhan University of Science and Technology Wuhan 430081 China School of Mathematics and Statistics Southwest University Chongqing 400715 China

In this paper, we study the circular cone eigenvalue complementarity problem (CCEiCP) by variational inequality technique, prove the existence of a solution to CCEiCP, and investigate different nonlinear programming formulations of the symmetric and asymmetric CCEiCP, respectively. We reduce CCEiCP to a variational inequality problem on a compact convex set, which guarantees that CCEiCP has at least one solution. Based on the variational inequality formulation of CCEiCP, the symmetric CCEiCP can be reformulated as a nonlinear programming problem NLP₁, and solved by computing a stationary point of the Rayleigh quotient function on a compact set. We formulate the asymmetric CCEiCP as another nonlinear programming problem NLP₂, and show that any global minimum of NLP₂ with an objective function value equal to zero is a solution of the asymmetric CCEiCP. Moreover, a stationary point of NLP₂ is a solution of the asymmetric CCEiCP, if and only if the Lagrange multipliers associated with the equalities in NLP₂ are equal to zero. The different formulations of CCEiCP provide alternative approaches for solving CCEiCP, which will play an important role in designing efficient algorithms to solve CCEiCP. © 2016, Chi et al.

关键词： circular cone eigenvalue complementarity problem nonlinear programming stationary point variational inequality formulation

Global contrast based salient region boundary sampling for action recognition 22nd

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Global contrast based salient region boundary sampling for a...

22nd International Conference on MultiMedia Modeling, MMM 2016

作者： Xu, Zengmin Hu, Ruimin Chen, Jun Chen, Huafeng Li, Hongyang National Engineering Research Center for Multimedia Software School of Computer Wuhan University Wuhan China Collaborative Innovation Center of Geospatial Technology Wuhan China School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Technology Guilin China

ISBN: (纸本)9783319276700

Although the excellent representation ability of improved Dense Trajectory (iDT) based features for action video had been proved on several action datasets, the performance of action recognition still suffers from large camera motion of videos. In this paper, we improve the iDT method by advancing a novel salient region boundary based dense sampling strategy, which reduces the number of trajectories while preserves the discriminative power. We first implement the iDT sampling based on motion boundary image, then introduce a global contrast based salient object segmentation method in interest points sampling step of action recognition. To overcome the flaws of global color contrast-based salient region sampling, we apply morphological gradient to generate a more robust mask for sampling dense points, as motion boundaries are much clearer. To evaluate the proposed method, we conduct extensive experiments on two benchmarks including HMDB51 and UCF 50. The results show that our sampling strategy can improve the performance of action recognition with minor computational cost of mask production. In particular, on the HMDB51 dataset, the improvement over the original iDT result is 3%. Meanwhile, any other dense features of action recognition can achieve more competitive performance by utilizing our sampling strategy and Fisher vector encoding method simply. © Springer International Publishing Switzerland 2016.

关键词： Trajectories