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981.
本文研究了Hermite矩阵特征值的任意扰动,给出了新的绝对和相对扰动界.所给出的界改进了Hoffman-Wielandt和Kahan早期的结果. 相似文献
982.
Salvatore A. Marano 《Proceedings of the American Mathematical Society》1997,125(10):2953-2961
For a family of elliptic eigenvalue problems with highly discontinuous nonlinearities, the existence of unbounded continua of positive solutions containing (0,0) is established by using techniques and results from set-valued analysis. Some special cases are then presented and discussed.
983.
Second-order finite-difference methods are developed for the numerical solutions of the eighth-, tenth- and twelfth-order
eigenvalue problems arising in the study of the effect of rotation on a horizontal layer of fluid heated from below. Instability
setting-in as overstability may be modelled by an eighth-order ordinary differential equation. When a uniform magnetic field
also acts across the fluid in the same direction as gravity, instability setting-in as ordinary convection may be modelled
by a tenth-order differential equation, while instability setting-in as overstability may be modelled by a twelfth-order differential
equation. The numerical methods are developed by making direct replacements of the derivatives in the differential equations
and then by computing the eigenvalues, which may incorporate Rayleigh number, horizontal wave speed and a time constant, from
the resulting algebraic eigenvalue problem. The eigenvalues are also computed by writing the differential equations as systems
of second-order differential equations and then using second- and fourth-order methods to obtain the eigenvalues. Numerical
results obtained using the two approaches are compared with estimates appearing in the literature. 相似文献
984.
谢建军 《高等学校计算数学学报(英文版)》1995,(1)
The problem of relating the eigervalues of an n×n Hermitian matrix to those of its Rayleigh-Ritz approximation is considered. The same residual bound for unitarily invariant norms on Hermilian matrices is obtained even without the orlhonormal and Rayleigh-Ritz assumptions in Stewart and Sun's book [9,Theorem IV. 4.14]. The result can also be extended to nearly Hermitian matrices. 相似文献
985.
李修清 《纯粹数学与应用数学》1998,14(2):71-75
引进了弱局部地角占优阵的概念,研究了这类矩阵的性质及其特征值问题,并给出了在稳定性理论中的应用。 相似文献
986.
987.
A semidefinite programming problem is a mathematical program in which the objective function is linear in the unknowns and the constraint set is defined by a linear matrix inequality. This problem is nonlinear, nondifferentiable, but convex. It covers several standard problems (such as linear and quadratic programming) and has many applications in engineering. Typically, the optimal eigenvalue multiplicity associated with a linear matrix inequality is larger than one. Algorithms based on prior knowledge of the optimal eigenvalue multiplicity for solving the underlying problem have been shown to be efficient. In this paper, we propose a scheme to estimate the optimal eigenvalue multiplicity from points close to the solution. With some mild assumptions, it is shown that there exists an open neighborhood around the minimizer so that our scheme applied to any point in the neighborhood will always give the correct optimal eigenvalue multiplicity. We then show how to incorporate this result into a generalization of an existing local method for solving the semidefinite programming problem. Finally, a numerical example is included to illustrate the results. 相似文献
988.
989.
本文首先对流形的测地球上的Sobolev常数进行讨论,并利用它进行Moser迭代,最终得到具有小负曲率的闭的黎曼流形上Laplace算子特征值的一个下界估计. 相似文献
990.
HU JiaxinDepartment of Mathematical Sciences Tsinghua University Beijing China 《中国科学A辑(英文版)》2004,47(5)
This paper investigates a class of nonlinear elliptic equations on a fractal domain. We establish a strong Sobolev-type inequality which leads to the existence of multiple non-trivial solutions of △u+ c(x)u = f(x, u), with zero Dirichlet boundary conditions on the Sierpihski gasket. Our existence results do not require any growth conditions of f(x,t) in t, in contrast to the classical theory of elliptic equations on smooth domains. 相似文献