共查询到20条相似文献,搜索用时 453 毫秒
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对具有内部构造安全保障体系的冗余机器系统中的特征值的存在性进行了分析求解,给出了实例,并对该系统的特征值进行了一个特征值对应一个特征向量的求征. 相似文献
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证明了由特征值及特征向量反求矩阵时,特征值在对角矩阵中的排序可以是任意的,只须将对应特征向量作相应排序,所得矩阵唯一。对于重特征值的线性无关的特征向量可任意选取,所得矩阵唯一。 相似文献
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提出了二环链系统,并利用二环链特征向量,给出了一个系统可实现二环链分解的充分必要条件,给出了可实现二环链线性系统的分解算法,研究了二环链系统的稳定性和能控性. 相似文献
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贵刊1991年12月发表高吉全同志“矩阵的特征根与特征向量的同步求解方法探讨”一文,阅后想提些改进意见,供大家参考。[1]是通过对n阶矩阵A的特征矩阼F(λ)施以列初等变换,将其化为下三角的λ—矩阵B(λ)来解决问题的。美中不足的是:设λ_0是A的一个特征根,当B(λ_0)中非0列向量线性相 相似文献
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In this paper we study the Galyorkin method with a special basis for a linear operator-differential equation of the third order in a separable Hilbert space. The projection method is based on the eigenvectors of the operator similar to the leading operator of equation. We obtain estimates for the convergence rate of approximate solutions in uniform topology. 相似文献
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本文给出Steklov特征值问题基于Legendre-Galerkin逼近的一种有效的谱方法.首先利用Legendre多项式构造了一组适当的基函数使得离散变分形式中的矩阵是稀疏的,然后推导了2维及3维情形下离散变分形式基于张量积的矩阵形式,由此可以快速地计算出离散的特征值和特征向量.文章还给出了误差分析和数值试验,数值结果表明本文提出的方法是稳定和有效的. 相似文献
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Fredrik Berntsson Anna Orlof Johan Thim 《Numerical Functional Analysis & Optimization》2017,38(3):293-305
The eigenvalue problem for linear differential operators is important since eigenvalues correspond to the possible energy levels of a physical system. It is also important to have good estimates of the error in the computed eigenvalues. In this work, we use spline interpolation to construct approximate eigenfunctions of a linear operator using the corresponding eigenvectors of a discretized approximation of the operator. We show that an error estimate for the approximate eigenvalues can be obtained by evaluating the residual for an approximate eigenpair. The interpolation scheme is selected in such a way that the residual can be evaluated analytically. To demonstrate that the method gives useful error bounds, we apply it to a problem originating from the study of graphene quantum dots where the goal was to investigate the change in the spectrum from incorporating electron–electron interactions in the potential. 相似文献
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Hans Zwart 《Journal of Differential Equations》2010,249(10):2397-2408
Given a Hilbert space and the generator of a strongly continuous group on this Hilbert space. If the eigenvalues of the generator have a uniform gap, and if the span of the corresponding eigenvectors is dense, then these eigenvectors form a Riesz basis (or unconditional basis) of the Hilbert space. Furthermore, we show that none of the conditions can be weakened. However, if the eigenvalues (counted with multiplicity) can be grouped into subsets of at most K elements, and the distance between the groups is (uniformly) bounded away from zero, then the spectral projections associated to the groups form a Riesz family. This implies that if in every range of the spectral projection we construct an orthonormal basis, then the union of these bases is a Riesz basis in the Hilbert space. 相似文献
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Min Ho Lee 《Acta Appl Math》1999,59(2):203-213
We construct Hecke operators acting on the space of certain linear ordinary differential equations, and describe a Hermitian inner product on the space of such differential equations. We also determine the adjoint of the Hecke operator with respect to this inner product, and prove that the space of ordinary differential equations associated to an automorphic form for a certain discrete subgroup of SL(2, R) has a basis consisting of common eigenvectors of a class of Hecke operators. 相似文献
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《Nonlinear Analysis: Hybrid Systems》2007,1(3):383-397
In this paper we consider the uniform stabilization of a vibrating string with Neumann-type boundary conditions. Herein we do not consider a controller stabilizing the system, but emphasize the simplicity and effectiveness of the controller. We adopt the linear feedback control law, which comprises both boundary velocity and position, and prove that the closed loop system is dissipative and asymptotically stable. By asymptotic analysis of frequency of the closed loop system, we give asymptotic expression of the frequencies and the Riesz basis property of eigenvectors and generalized eigenvectors of the system operator under some conditions, and hence obtain the exponential stability of the closed loop system. We show that, for a particular case, the system may be super-stable in subspace of a codimensional one. From the above result, we conclude that one can design a much simpler linear controller by choice of parameters such that the closed loop system is of Riesz basic properties and exponentially stable. 相似文献
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In this paper we study the basis property of root vectors of a star-shaped networks of strings whose exterior ends are clamped
and common node has a damping. The main operator determined by the networks is non-normal. By the asymptotical technique,
we show that its spectra distribute in a strip parallel to the imaginary axis, and there is a sequence of root vectors (generalized
eigenvectors and eigenvectors) that forms a Riesz basis with parentheses for the Hilbert state space. As a application of
this result, we discuss the stability of the system. 相似文献
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Sensitivity analysis of linear vibration system is of wide interest. In this paper, sensitivity analysis based on non-defective system and defective system is summarized in all cases. Specially, for the defective systems, a fast method for the perturbation problem of state vectors is constructed in terms of the theories of generalized eigenvectors and adjoint matrices. By this method, the state vector derivatives can be expressed by a linear combination of generalized eigenvectors. The expansion coefficients can be obtained without solving large-scale equations based on eigensolutions of original system. Numerical results demonstrate the effectiveness and the stability of the method. 相似文献
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In this paper we study the properties of a kurtosis matrix and propose its eigenvectors as interesting directions to reveal the possible cluster structure of a data set. Under a mixture of elliptical distributions with proportional scatter matrix, it is shown that a subset of the eigenvectors of the fourth-order moment matrix corresponds to Fisher’s linear discriminant subspace. The eigenvectors of the estimated kurtosis matrix are consistent estimators of this subspace and its calculation is easy to implement and computationally efficient, which is particularly favourable when the ratio n/p is large. 相似文献
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It is commonplace in many application domains to utilize polynomial eigenvalue problems to model the behaviour of physical systems. Many techniques exist to compute solutions of these polynomial eigenvalue problems. One of the most frequently used techniques is linearization, in which the polynomial eigenvalue problem is turned into an equivalent linear eigenvalue problem with the same eigenvalues, and with easily recoverable eigenvectors. The eigenvalues and eigenvectors of the linearization are usually computed using a backward stable solver such as the QZ algorithm. Such backward stable algorithms ensure that the computed eigenvalues and eigenvectors of the linearization are exactly those of a nearby linear pencil, where the perturbations are bounded in terms of the machine precision and the norms of the matrices defining the linearization. Although we have solved a nearby linear eigenvalue problem, we are not certain that our computed solution is in fact the exact solution of a nearby polynomial eigenvalue problem. Here, we perform a backward error analysis for the solution of a specific linearization for polynomials expressed in the monomial basis. We use a suitable one-sided factorization of the linearization that allows us to map generic perturbations of the linearization onto structured perturbations of the polynomial coefficients. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献