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Symplectic eigenvector expansion theorem of a class of operator matrices arising from elasticity theory

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Chinese Physics B 2011年第1期20卷 92-97页

作者：王华阿拉坦仓黄俊杰 School of Mathematical Sciences Inner Mongolia University College of Sciences Inner Mongolia University of Technology

This paper deals with the completeness of the eigenvector system of a class of operator matrices arising from elasticity theory, i.e., symplectic eigenvector expansion theorem. Under certain conditions, the symplectic orthogonality of eigenvectors of the operator matrix is demonstrated. Based on this, a necessary and sufficient condition for the completeness of the eigenvector system of the operator matrix is given. Furthermore, the obtained results are tested for the free vibration of rectangular thin plates.

关键词： operator matrix eigenvector completeness eigenvector expansion theorem

Left eigenvector of a Stochastic Matrix

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Advances in Pure Mathematics 2011年第4期1卷 105-117页

作者： Sylvain Lavalle′e 不详

We determine the left eigenvector of a stochastic matrix M associated to the eigenvalue 1 in the commutative and the noncommutative cases. In the commutative case, we see that the eigenvector associated to the eigenvalue 0 is (N1,Nn) , where Ni is the i–th iprincipal minor of N=M–In , where In is the identity matrix of dimension n. In the noncommutative case, this eigenvector is (P1-1,Pn-1) , where Pi is the sum in Q《αij》 of the corresponding labels of nonempty paths starting from i and not passing through i in the complete directed graph associated to M .

关键词： Generic Stochastic Noncommutative Matrix Commutative Matrix Left eigenvector Associated To The Eigenvalue 1 Skew Field Automata

A Modified eigenvector Method for Blind Deconvolution of MIMO Systems Using the Matrix Pseudo-Inversion Lemma

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Circuits and Systems 2011年第1期2卷 7-13页

作者： Mitsuru Kawamoto Kiyotaka Kohno Yujiro Inouye Koichi Kurumatani 不详

Recently we have developed an eigenvector method (EVM) which can achieve the blind deconvolution (BD) for MIMO systems. One of attractive features of the proposed algorithm is that the BD can be achieved by calculating the eigenvectors of a matrix relevant to it. However, the performance accuracy of the EVM depends highly on computational results of the eigenvectors. In this paper, by modifying the EVM, we propose an algorithm which can achieve the BD without calculating the eigenvectors. Then the pseudo-inverse which is needed to carry out the BD is calculated by our proposed matrix pseudo-inversion lemma. Moreover, using a combination of the conventional EVM and the modified EVM, we will show its performances comparing with each EVM. Simulation results will be presented for showing the effectiveness of the proposed methods.

关键词： Blind Signal Processing Blind Deconvolution eigenvector Methods Super-Exponential Mthods MIMO Systems Matrix Pseudo-Inversion Lemma

A Decorrelating DOA Estimation Based on the Principal eigenvector for CDMA Frequency-Selective Fading Channels

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Journal of Southeast University(English Edition) 2001年第2期17卷 14-17页

作者：杨维蒋朱成程时昕东南大学移动通信国家重点实验室南京210096

A novel decorrelating DOA estimation algorithm of multipath signals for CDMA frequency selective fading channels based only on the principal eigenvector of its corresponding covariance matrix is proposed. The proposed algorithm has the advantages that the DOAs of the multipath signals can be estimated independently and all the other resolved multipath signal interference is eliminated. Simulation results show that this algorithm estimates the DOAs of multipath signals efficiently and accurately. 

关键词： decorrelating DOA estimation antenna array CDMA system eigenvector

类星体中射电强度与eigenvector 1的关系

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天津师范大学学报（自然科学版） 2017年第4期37卷 20-24页

作者：王永江商朝晖天津师范大学物理与材料科学学院天津300387

为揭示射电强度R与eigenvector1的联系,以SDSSDR7中的类星体源为母样本,通过限制基础物理参数黑洞质量和爱丁顿吸积率的范围选择研究样本,并根据射电强度R将样本分为不同的区间建立复合谱,用以探究eigenvector1中典型观测参数随射电强度... 详细信息

为揭示射电强度R与eigenvector1的联系,以SDSSDR7中的类星体源为母样本,通过限制基础物理参数黑洞质量和爱丁顿吸积率的范围选择研究样本,并根据射电强度R将样本分为不同的区间建立复合谱,用以探究eigenvector1中典型观测参数随射电强度R的变化.结果表明:射电强度只与[OⅢ]线的强度正相关,而与光学FeⅡ线强度无关,说明射电辐射只是eigenvector1中的二级过程,不是驱动因素.

关键词：射电强度 eigenvector 1 [OⅢ]发射线光学FeⅡ发射线类星体

IMPROVING eigenvectorS IN ARNOLDI'S METHOD

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Journal of Computational Mathematics 2000年第3期18卷 265-276页

作者： Zhong-xiao Jia (Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China) Ludwig Elsner (Fakultat fur Mathematik, University Bielefeld, Postfach 100131, 33501 Bielefeld,Germany) 大连理工大学辽宁大连 116024 Universitt Bielefeld 德国 Bielefeld 33501

The Ritz vectors obtained by Arnoldi's method may not be good approxima- tions and even may not converge even if the corresponding Ritz values do. In order to improve the quality of Ritz vectors and enhance the efficiency of Arnoldi type algorithms, we propose a strategy that uses Ritz values obtained from an m-dimensional Krylov subspace but chooses modified approximate eigenvectors in an (m + 1)-dimensional Krylov subspace. Residual norm of each new approximate eigenpair is minimal over the span of the Ritz vector and the (m+1)th basis vector, which is available when the m-step Arnoldi process is run. The resulting modi- fied m-step Arnoldi method is better than the standard m-step one in theory and cheaper than the standard (m + 1)-step one. Based on this strategy, we present a modified m-step restarted Arnoldi algorithm. Numerical examples show that the modified m-step restarted algorithm and its version with Chebyshev acceleration are often considerably more efficient than the standard (m+ 1)-step restarted ones.

关键词： Large unsymmetric The m-step Arnoldi process The m-step Arnoldi method Eigenvalue Ritz value eigenvector Ritz vector Modified

DGMRES Method Augmented with eigenvectors for Computing the Drazin-inverse Solution of Singular Linear Systems

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Acta Mathematicae Applicatae Sinica 2016年第2期32卷 549-558页

作者： Bin MENG College of Science Nanjing University of Aeronautics and Astronautics

The DGMRES method for solving Drazin-inverse solution of singular linear systems is generally used with restarting. But the restarting often slows down the convergence and DGMRES often stagnates. We show that adding some eigenvectors to the subspace can improve the convergence just like the method proposed by R. Morgan in [R. Morgan, A restarted GMRES method augmented with eigenvectors, SIAM J. Matrix Anal App1., 16： 1154-1171, 1995. We derive the implementation of this method and present some numerical examples to show the advantages of this method.

关键词： Drazin-inverse DGMRES Krylov subspace iterative method eigenvector

Nondegeneracy of eigenvectors and singular vector tuples of tensors

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Science China Mathematics 2022年第12期65卷 2483-2492页

作者： Shenglong Hu Department of Mathematics School of ScienceHangzhou Dianzi UniversityHangzhou 310018China

In this article, nondegeneracy of singular vector tuples, Z-eigenvectors and eigenvectors of tensors is studied, which have found many applications in diverse areas. The main results are:(ⅰ)each(Z-)eigenvector/singular vector tuple of a generic tensor is nondegenerate, and(ⅱ) each nonzero Zeigenvector/singular vector tuple of an orthogonally decomposable tensor is nondegenerate.

关键词： tensor singular vector tuple eigenvector Z-eigenvector nondegeneracy generic

COMPUTING THE eigenvectorS OF A MATRIX WITH MULTIPLEX EIGENVALUES BY SVD METHOD

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Applied Mathematics and Mechanics(English Edition) 2004年第3期25卷 257-262页

作者：迟彬叶庆凯 Department of Mechanics and Engineering Science Peking University

Every matrix is similar to a matrix in Jordan canonical form,which has very important sense in the theory of linear algebra and its engineering *** a matrix with multiplex eigenvalues,an algorithm based on the singular value decomposition(SVD) for computing its eigenvectors and Jordan canonical form was *** simulation shows that this algorithm has good effect in computing the eigenvectors and its Jordan canonical form of a matrix with multiplex *** is superior to MATLAB and MATHEMATICA.

关键词： multiplex eigenvalue eigenvector eigenvector chain Jordan canonical form