共查询到20条相似文献,搜索用时 15 毫秒
1.
《Journal of Complexity》1993,9(3):387-405
We apply a novel approach to approximate within ϵ to all the eigenvalues of an n × n symmetric tridiagonal matrix A using at most n2([3 log2(625n6)] + (83n − 34)[log2 (log2((λ1 − λn)/(2ϵ))/log2(25n))]) arithmetic operations where λ1 and λn denote the extremal eigenvalues of A. The algorithm can be modified to compute any fixed numbers of the largest and the smallest eigenvalues of A and may also be applied to the band symmetric matrices without their reduction to the tridiagonal form. 相似文献
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§1.引言 [3]曾提出两类Hermiie阵的代数特征值反问题,后来被人们称之为加法问题和乘法问题并推广到更一般的情形.到目前止,经典代数特征值反问题在数学上的最一般提法如下: 问题G.给定n+1个n阶实对称矩阵A,A_1,…,A_n和n个实数λ_1,…,λ_n,求n个实数x_1,…,x_n,使矩阵 相似文献
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This paper describes a method of obtaining all or a dominantsubset of the eigenvalues and corresponding left and right-handeigenvectors of unsymmetric matrices by simultaneous iteration.The method differs from Bauer's biiteration in that re-orientationof the trial vectors is achieved at each iteration by performingan "interaction analysis". 相似文献
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Da-Yong Cai & Jing Hong 《计算数学(英文版)》1989,7(3):313-320
In this paper, a new algorithm for the eigenvalue problem of matrices is given. Numerical examples show that it could be a remarkable approach for practical purposes. Some open problems are listed. 相似文献
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《数学的实践与认识》2019,(24)
对Helmholtz传输特征值问题,在Cakoni等提出的混合变分公式的基础上,给出了一种谱混合法并作了相应的误差分析.报道了二维和三维区域的数值试验,计算出了高精度的实和复传输特征值.数值结果表明这种方法的高效性. 相似文献
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This paper proposes a new and efficient method for “Escherization”, that is, for generating a tile which is close to a given
shape and whose copies cover the plane without gaps or overlaps except at their boundaries. In this method, the Escherization
problem is reduced to a maximum eigenvalue problem, which can be solved easily, while the existing method requires time consuming
heuristic search. Furthermore, we show that the optimal shape corresponds to the orthogonal projection of the vector representing
the given shape to the “space of tilable shapes”. 相似文献
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A generalization of the Rayleigh quotient iterative method,called the Minimum Residual Quotient Iteration (MRQI), is derivedfor the numerical solution of the 2-parameter eigenvalue problem;i.e. to find scalars µ and a corresponding vector x satisfyingthe following equations, Ax = B1x + µB2x, ||x|| = 1, f(x) = 0, where A and B are nxn real matrices, ||.|| denotes the l2 normand f is a real functional. The method is applied to doubleeigenvalue problems for ordinary differential equations andcomputational results are presented. 相似文献
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This paper studies the spectral properties of the partial differential operator over a finite region Ω. This operator, which arises in the analysis of nonaxisymmetric, rapidly rotating compressible flows, is treated as a perturbation of the operator which is generated by the terms Using the fact that , when defined on a suitable domain, is closed and self-adjoint, it is shown that [when acting on elements of ] is an operator with compact resolvent whose generalized eigenvectors are complete in ?2 (Ω). 相似文献
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类p-Laplacian方程的特征值问题 总被引:7,自引:1,他引:7
本文考虑类p-Laplacian方程-div(a(|Du|~p)|Du|~(p-2)Du)=λf(x,u),x∈Ω,u=0,x∈Ω的特征值问题,其中ΩR~n(n≥2)是有界光滑区域.当λ>0充分小,本质上仅在凸函数的假设下,得到了性质完全不同的两个特征函数的存在性,作为定理的应用,文中给出了两个实例. 相似文献
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实对称矩阵的特征值问题,无论是低阶稠密矩阵的全部特征值问题,或高阶稀疏矩阵的部分特征值问题,都已有许多有效的计算方法,迄今最重要的一些成果已总结在[5]中。本文利用规范矩阵的一些重要性质将对于Hermite矩阵(特别是对弥矩阵)特征值问题的一些有效算法推广到规范矩阵的特征值问题,由于对复规范阵的推广是简单的,而且实际上常遇到的是实矩阵(这时常要求只用实运算),因此我们着重讨论实规范矩阵的特征值问题。 相似文献
14.
Diego Armentano 《Foundations of Computational Mathematics》2014,14(2):185-236
A unitarily invariant projective framework is introduced to analyze the complexity of path-following methods for the eigenvalue problem. A condition number, and its relation to the distance to ill-posedness, is given. A Newton map appropriate for this context is defined, and a version of Smale’s $\gamma $ -theorem is proven. The main result of this paper bounds the complexity of path-following methods in terms of the length of the path in the condition metric. 相似文献
15.
Shu-Fang Xu 《计算数学(英文版)》1993,11(1):7-19
A homotopy algorithm for solving the inverse eigenvalue problem for complex symmetric matrices is suggested. Some numerical examples are presented. 相似文献
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针对具有四个状态的系统所建立的模型,得出了系统算子一个特征值对应一个特征向量的结论,并证明了除0特征外还存在另外非零实特征值. 相似文献
18.
The nonlinear eigenvalue problem for p-Laplacian is considered. We assume that 1 < p < N and that the function f is of subcritical growth with respect to the variable u. The existence and C1,α-regularity of the weak solution is proved. 相似文献
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The optimization problem with the Bilinear Matrix Inequality (BMI) is one of the problems which have greatly interested researchers of system and control theory in the last few years. This inequality permits to reduce in an elegant way various problems of robust control into its form. However, in contrast to the Linear Matrix Inequality (LMI), which can be solved by interior-point-methods, the BMI is a computationally difficult object in theory and in practice. This article improves the branch-and-bound algorithm of Goh, Safonov and Papavassilopoulos (Journal of Global Optimization, vol. 7, pp. 365–380, 1995) by applying a better convex relaxation of the BMI Eigenvalue Problem (BMIEP), and proposes new Branch-and-Bound and Branch-and-Cut Algorithms. Numerical experiments were conducted in a systematic way over randomly generated problems, and they show the robustness and the efficiency of the proposed algorithms. 相似文献