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

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.

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

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.

EIGENVECTORS OF SYSTEM OF HAMMERSTEIN INTEGRAL EQUATIONS IN BANACH SPACES ANDAPPLICATIONS

In this paper, the author investigates the existence of eigenvectors of system of Hammerstein integral equations in Banach spaces by means of fixed point index theory. He also gives some applications to a system of S turm-Liouville problems of ordinary differential equations.

Eigenvectors of Permutation Matrices

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.

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

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.

Floquet Eigenvectors Theory of Pulsed Bias Phase and Quadrature Harmonic Oscillators

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.

Derivatives of repeated eigenvalues and corresponding eigenvectors of damped systems

A procedure is presented for computing the derivatives of repeated eigenvalues and the corresponding eigenvectors of damped systems. The derivatives are calculated in terms of the eigenvalues and eigenvectors of the second-order system, and the use of rather undesirable state space representation is avoided. Hence the cost of computation is greatly reduced. The efficiency of the proposed procedure is illustrated by considering a 5-DOF non-proportionally damped system.

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

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 application.For a matrix with multiplex eigenvalues,an algorithm based on the singular value decomposition(SVD) for computing its eigenvectors and Jordan canonical form was proposed.Numerical simulation shows that this algorithm has good effect in computing the eigenvectors and its Jordan canonical form of a matrix with multiplex eigenvalues.It is superior to MATLAB and MATHEMATICA.

Time Eigenvectors and Their Applications

Time eigenvectors and time operator are constructed from energy eigenvectors of system.Some features of them are described.Their applications to harmonic oscillating system and to double wave description of system are discussed.

Some Properties of Eigenvalues and Eigenvectors of Wilkinson Matrices

Some properties of characteristic polynomials, eigenvalues, and eigenvectors of the Wilkinson matrices W2n＋1 and W2n＋1 are presented. It is proved that the eigenvalues of W2n＋1 just are the eigenvalues of its leading principal submatrix Vn and a bordered matrix of Vn. Recurrence formula are given for the characteristic polynomial of W2＋n＋1 . The eigenvectors of W2＋n＋1 are proved to be symmetric or skew symmetric. For W2n＋1 , it is found that its eigenvalues are zero and the square roots of the eigenvalues of a bordered matrix of Vn2. And the eigenvectors of W2n＋1 , which the corresponding eigenvahies are opposite in pairs, have close relationship.

On Monotone Eigenvectors of a Max-<i>T </i>Fuzzy Matrix

The eigenvectors of a fuzzy matrix correspond to steady states of a complex discrete-events system, characterized by the given transition matrix and fuzzy state vectors. The descriptions of the eigenspace for matrices in the max-Lukasiewicz algebra, max-min algebra, max-nilpotent-min algebra, max-product algebra and max-drast algebra have been presented in previous papers. In this paper, we investigate the monotone eigenvectors in a max-T algebra, list some particular properties of the monotone eigenvectors in max-Lukasiewicz algebra, max-min algebra, max-nilpotent-min algebra, max-product algebra and max-drast algebra, respectively, and illustrate the relations among eigenspaces in these algebras by some examples.

On Edge Singularity and Eigenvectors of Mixed Graphs

Let G be a mixed glaph which is obtained from an undirected graph by orienting some of its edges. The eigenvalues and eigenvectors of G are, respectively, defined to be those of the Laplacian matrix L（G） of G. As L（G） is positive semidefinite, the singularity of L（G） is determined by its least eigenvalue λ1 （G）. This paper introduces a new parameter edge singularity εs（G） that reflects the singularity of L（G）, which is the minimum number of edges of G whose deletion yields that all the components of the resulting graph are singular. We give some inequalities between εs（G） and λ1 （G） （and other parameters） of G. In the case of εs（G） = 1, we obtain a property on the structure of the eigenvectors of G corresponding to λ1 （G）, which is similar to the property of Fiedler vectors of a simple graph given by Fiedler.

CONVERGENCE OF ALGORITHMS FOR FINDING EIGENVECTORS

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.

IMPROVING EIGENVECTORS IN ARNOLDI'S METHOD

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.

COMPUTING EIGENVECTORS OF NORMAL MATRICES WITH SIMPLE INVERSE ITERATION

It is well-known that if we have an approximate eigenvalue A of a normal matrix A of order n, a good approximation to the corresponding eigenvector u can be computed by one inverse iteration provided the position, say kmax, of the largest component of u is known. In this paper we give a detailed theoretical analysis to show relations between the eigenvector u and vector Xk, k = 1, … ,n, obtained by simple inverse iteration, i.e., the solution to the system (A - I)x = ek with ek the kth column of the identity matrix I. We prove that under some weak conditions, the index kmax is of some optimal properties related to the smallest residual and smallest approximation error to u in spectral norm and Probenius norm. We also prove that the normalized absolute vector v = |u|/||u|| of u can be approximated by the normalized vector of (||x1||2, … ||xn||2)T- We also give some upper bounds of |u(k)| for those 'optimal' indexes such as Fernando's heuristic for kmax without any assumptions. A stable double orthogonal factorization method and a simpler but may less stable approach are proposed for locating the largest component of u.

Nondegeneracy of eigenvectors and singular vector tuples of tensors

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.

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

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.

Multi-attribute decision-making based on subjective and objective integrated eigenvector method

An integrated approach is proposed to investigate the fuzzy multi-attribute decision-making （MADM） problems, where subjective preferences are expressed by a pairwise comparison matrix on the relative weights of attributes and objective information is expressed by a decision matrix. An eigenvector method integrated the subjective fuzzy preference matrix and objective information is proposed. Two linear programming models based on subjective and objective information are introduced to assess the relative importance weights of attributes in an MADM problem. The simple additive weighting method is utilized to aggregate the decision information, and then all the alternatives are ranked. Finally, a numerical example is given to show the feasibility and effectiveness of the method. The result shows that it is easier than other methods of integrating subjective and objective information.

PHASE AUTOFOCUSING ALGORITHM FOR COMPRESSED INVERSE SYNTHETIC APERTURE RADAR IMAGING

As same as the conventional inverse synthetic aperture radar（ISAR）, the compressed ISAR also requires the echo signal based motion compensation, which consists of the range alignment and the phase autofoeusing. A phase autofocusing algorithm for compressed ISAR imaging is presented. In the algorithm, phase autofocusing for the sparse ISAR echoes is accomplished using the eigenvector method. Experimental results validate the effectiveness of the algorithm.

Ensemble Retrieval of Atmospheric Temperature Profiles from AIRS

ABSTRACT Satellite-based observations provide great opportunities for improving weather forecasting. Physical retrieval of atmo spheric profiles from satellite observations is sensitive to the uncertainty of the first guess and other factors. In order to improve the accuracy of the physical retrieval, an ensemble methodology was developed with an emphasis on perturbing the first guess. In the methodology, a normal probability density function （PDF） is used to select the optimal profile from the ensemble retrievals. The ensemble retrieval algorithm contains four steps： （1） regression retrieval for original first guess; （2） perturbation of the original first guess to generate new first guesses （ensemble first guesses）; （3） using the ensemble first guesses and nonlinear iterative physical retrieval to generate ensemble physical results; and （4） the final optimal profile is selected from the ensemble physical results by using PDE Temperature eigenvectors （EVs） were used to generate the pertur- bation and generate the ensemble first guess. Compared with the regular temperature profile retrievals from the Atmospheric InfraRed Sounder （AIRS）, the ensemble retrievals RMSE of temperature profiles selected by the PDF was reduced between 150 and 320 hPa and below 400 hPa, with a maximum improvement of 0.3 K at 400 hPa. The bias was also reduced in many layers, with a maximum improvement of 0.69 K at 460 hPa. The combined optimal （CombOpt） profile and a mean optimal （MeanOpt） profile of all ensemble physical results were improved below 150 hPa. The MeanOpt profile was better than the CombOpt profile, and was regarded as the final optimal （FinOpt） profile. This study lays the foundation for improving temperature retrievals from hyper-spectral infrared radiance measurements.