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CONVERGENCE OF ALGORITHMS FOR FINDING eigenvectors

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Acta Mathematicae Applicatae Sinica 2000年第4期16卷 355-361页

作者：张俊华 Institute of Applied Mathematics the Academy of Mathematics and Systems Siciences the Chinese Academy of Sciences Beijing China

In this paper we give a rigorous analysis of convergence of algorithms for finding eigenvectors of a real symmetric matrix. The algorithms are deterministic and our methods are very intuitive.

关键词： eigenvectors algorithms convergence

A Construction of Multi-Sender Authentication Codes from Eigenvalues and eigenvectors of the Matrix Over Finite Fields

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Journal of Harbin Institute of Technology(New Series) 2019年第1期26卷 51-60页

作者： Xiuli Wang Lina Wang Yakun Hao College of Science Civil Aviation University of China

We construct one multi-sender authentication code by algebraic combination method from eigenvalues and eigenvectors of the matrix over nite elds. Some parameters and the probabilities of three kinds of successful attack of this code are also computed. For multi-sender authentication code,it allows a group of senders to construct an authenticated message for a receiver such that the receiver can verify authenticity of the received message.

关键词： multi-sender authentication codes nonsingular symmetric matrix eigenvalues eigenvectors finite fields

eigenvectors of Permutation Matrices

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Advances in Pure Mathematics 2015年第7期5卷 390-394页

作者： M. Isabel Garca-Planas M. Dolors Magret Departament de Matemàtica Aplicada I Universitat Politècnica de Catalunya Barcelona Spain

The spectral properties of special matrices have been widely studied, because of their applications. We focus on permutation matrices over a finite field and, more concretely, we compute the minimal annihilating polynomial, and a set of linearly independent eigenvectors from the decomposition in disjoint cycles of the permutation naturally associated to the matrix.

关键词： Permutation Matrices Eigenvalues eigenvectors

Floquet eigenvectors Theory of Pulsed Bias Phase and Quadrature Harmonic Oscillators

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Circuits and Systems 2012年第1期3卷 72-81页

作者： Fabrizio Palma Stefano Perticaroli 不详

The paper presents an analytical derivation of Floquet eigenvalues and eigenvectors for a class of harmonic phase and quadrature oscillators. The derivation refers in particular to systems modeled by two parallel RLC resonators with pulsed energy restoring. Pulsed energy restoring is obtained through parallel current generators with an impulsive characteristic triggered by the resonators voltages. In performing calculation the initial hypothesis of the existence of stable oscillation is only made, then it is verified when both oscillation amplitude and eigenvalues/eigenvectors are deduced from symmetry conditions on oscillator space state. A detailed determination of the first eigenvector is obtained. Remaining eigenvectors are hence calculated with realistic approximations. Since Floquet eigenvectors are acknowledged to give the correct decomposition of noise perturbations superimposed to the oscillator space state along its limit cycle, an analytical and compact model of their behavior highlights the unique phase noise properties of this class of oscillators.

关键词： Floquet eigenvectors Noise Decomposition Phase and Quadrature Oscillators Pulsed Bias Oscillator Oscillator Phase Noise

A Unified Algebraic Technique for Eigenvalues and eigenvectors in Quaternionic and Split Quaternionic Mechanics

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Journal of Applied Mathematics and Physics 2019年第9期7卷 1929-1940页

作者： Zhenwei Guo Gang Wang Dong Zhang Tongsong Jiang School of Mathematical Science Liaocheng University Liaocheng China College of Mathematics and Systems Science Shandong University of Science and Technology Qingdao China School of Mathematics and Statistics Heze University Heze China

This paper aims to present, in a unified manner, the algebraic techniques of eigen-problem which are valid on both the quaternions and split quaternions. This paper studies eigenvalues and eigenvectors of the v-quaternion matrices by means of the complex representation of the v-quaternion matrices, and derives an algebraic technique to find the eigenvalues and eigenvectors of v-quaternion matrices. This paper also gives a unification of algebraic techniques for eigenvalues and eigenvectors in quaternionic and split quaternionic mechanics.

关键词： v-Quaternion Complex Representation Quaternion Split Quaternion Eigenvalues eigenvectors

Derivation of Floquet eigenvectors Displacement for Optimal Design of LC Tank Pulsed Bias Oscillators

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Circuits and Systems 2011年第4期2卷 311-319页

作者： Stefano Perticaroli Nikend Luli Fabrizio Palma 不详

The paper presents an approximated and compact derivation of the mutual displacement of Floquet eigenvectors in a class of LC tank oscillators with time varying bias. In particular it refers to parallel tank oscillators of which the energy restoring can be modeled through a train of current pulses. Since Floquet eigenvectors are acknowledged to give a correct decomposition of noise perturbations along the stable orbit in oscillator's space state, an analytical and compact model of their displacement can provide useful criteria for designers. The goal is to show, in a simplified case, the achievement of oscillators design oriented by eigenvectors. To this aim, minimization conditions of the effect of stationary and time varying noise as well as the contribution of jitter noise introduced by driving electronics are deduced from analytical expression of eigenvectors displacement.

关键词： Floquet eigenvectors Noise Decomposition Pulsed Bias Oscillator Oscillator Phase Noise

Development of basic technique to improve seismic response accuracy of tributary area-based lumped-mass stick models

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Earthquake Engineering and Engineering Vibration 2019年第1期18卷 113-127页

作者： Yu-Chen Ou Ibrahim Hashlamon WooSeok Kim Hwasung Roh Department of Civil Engineering Taiwan University (NTU) Department of Civil Engineering Chonbuk National University Department of Civil Engineering Chungnam National University

Although a detailed finite element(FE) model provides more precise results, a lumped-mass stick(LMS) model is preferred because of its simplicity and rapid computational time. However, the reliability of LMS models has been questioned especially for structures dominated by higher modes and seismic inputs. Normally, the natural frequencies and dynamic responses of a LMS model based on tributary area mass consideration are different from the results of the FE model. This study proposes a basic updating technique to overcome these discrepancies; the technique employs the identical modal response, D(t), to the detailed FE model. The parameter D(t) is a time variable function in the dynamic response composition and it depends on frequency and damping ratio for each mode, independent of the structure's mode shapes. The identical response D(t) for each mode is obtained from the frequency adaptive LMS model; the adaptive LMS model which can provide identical modal frequencies as the detailed FE model. Theoretical backgrounds and formulations of the updating technique are proposed. To validate the updating technique, two types of structures(a symmetric straight column and an unsymmetric T-shaped structure) are considered. From the seismic response results including base shear and base moment, the updating technique considerably improves the seismic response accuracy of the tributary area-based LMS model.

关键词： lumped-mass stick models seismic responses modal frequency eigenvectors response accuracy

Certifying the Global Optimality of Quartic Minimization over the Sphere

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Journal of the Operations Research Society of China 2022年第2期10卷 241-287页

作者： Sheng-Long Hu Department of Mathematics School of ScienceHangzhou Dianzi UniversityHangzhou 310018ZhejiangChina

The quartic minimization over the sphere is an NP-hard problem in the general *** exist various methods for computing an approximate solution for any given *** practice,it is quite often that a global optimal solution was found but without a *** will present in this article two classes of methods which are able to certify the global optimality,i.e.,algebraic methods and semidefinite program(SDP)relaxation *** advances on these topics are summarized,accompanied with some emerged new *** want to emphasize that for mediumor large-scaled instances,the problem is still a challenging one,due to an apparent limitation on the current force for solving SDP problems and the intrinsic one on the approximation techniques for the problem.

关键词： Quartic minimization Tensor Sphere Global optimality Elimination method Critical points eigenvectors Determinant Nondegenerate Characteristic polynomial SDP relaxations Moment matrix Flatness Positivstellensatz Nonnegative polynomial Sums of squares Duality

Composite orthogonal projection methods for large matrix eigenproblems

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Science China Mathematics 1999年第6期42卷 577-585页

作者：贾仲孝 Department of Applied Mathematics Dalian University of Technology Dalian China

For classical orthogonal projection methods for large matrix eigenproblems, it may be much more difficult for a Ritz vector to converge than for its corresponding Ritz value when the matrix in question is non-Hermitian. To this end, a class of new refined orthogonal projection methods has been proposed. It is proved that in some sense each refined method is a composite of two classical orthogonal projections, in which each refined approximate eigenvector is obtained by realizing a new one of some Hermitian semipositive definite matrix onto the same subspace. A priori error bounds on the refined approximate eigenvector are established in terms of the sine of acute angle of the normalized eigenvector and the subspace involved. It is shown that the sufficient conditions for convergence of the refined vector and that of the Ritz value are the same, so that the refined methods may be much more efficient than the classical ones.

关键词： classical orthogonal projection refined orthogonal projection Ritz values Ritz vectors refined approximate eigenvectors convergence