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71.
72.
The bound on remainder term in CLT for a sum of independent random variables taking values in Hilbert space is obtained. This bound sharpens the result due to Bentkus and Götze. 相似文献
73.
Let x:M → Rn be an umbilical free hypersurface with non-zero principal curvatures.Then x is associated with a Laguerre metric g,a Laguerre tensor L,a Laguerre form C,and a Laguerre second fundamental form B,which are invariants of x under Laguerre transformation group.An eigenvalue of Laguerre tensor L of x is called a Laguerre eigenvalue of x.In this paper,we classify all oriented hypersurfaces with constant Laguerre eigenvalues and vanishing Laguerre form. 相似文献
74.
Francisco M. Fernández 《International journal of quantum chemistry》2009,109(4):717-719
We show that the connected‐moments polynomial approach proposed recently is equivalent to the well known Rayleigh–Ritz variation method in the Krylov space. We compare the latter with one of the original connected‐moments methods by means of a numerical test on an anharmonic oscillator. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 相似文献
75.
De Tong Zhu 《数学学报(英文版)》2008,24(12):2081-2100
We extend the classical affine scaling interior trust region algorithm for the linear constrained smooth minimization problem to the nonsmooth case where the gradient of objective function is only locally Lipschitzian. We propose and analyze a new affine scaling trust-region method in association with nonmonotonic interior backtracking line search technique for solving the linear constrained LC1 optimization where the second-order derivative of the objective function is explicitly required to be locally Lipschitzian. The general trust region subproblem in the proposed algorithm is defined by minimizing an augmented affine scaling quadratic model which requires both first and second order information of the objective function subject only to an affine scaling ellipsoidal constraint in a null subspace of the augmented equality constraints. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions where twice smoothness of the objective function is not required. Applications of the algorithm to some nonsmooth optimization problems are discussed. 相似文献
76.
In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local maximum, we utilize a merit function to guide the iterates toward a local minimum. Especially, we add the parameter ε to the Newton system when calculating the decrease directions. The global convergence is achieved by the decrease of a merit function. Furthermore, the numerical results confirm that the algorithm can solve this kind of problems in an efficient way. 相似文献
77.
In this paper, we study a second order variational problem for locally convex hypersurfaces, which is the affine invariant analogue of the classical Plateau problem for minimal surfaces. We prove existence, regularity and uniqueness results for hypersurfaces maximizing affine area under appropriate boundary conditions.
78.
A. Melman. 《Mathematics of Computation》2001,70(234):649-669
We exploit the even and odd spectrum of real symmetric Toeplitz matrices for the computation of their extreme eigenvalues, which are obtained as the solutions of spectral, or secular, equations. We also present a concise convergence analysis for a method to solve these spectral equations, along with an efficient stopping rule, an error analysis, and extensive numerical results.
79.
A new method for estimating bounds of eigenvalues 总被引:1,自引:0,他引:1
A new method for estimating the bounds of eigenvalues is presented. In order to show that the method proposed is as effective
as Qiu's, an undamping spring-mass system with 5 nodes and 5 degrees of freedom is given. To illustrate that the present method
can be applied to structures which cannot be treated by non-negative decomposition, a plane frame with 202 nodes and 357 beam
elements is given. The results show that the present method is effective for estimating the bounds of eigenvalues and is more
common than Qiu's.
Project supported by the National Natural Science Foundation (No. 19872028) and the Mechanical Technology Development Foundation
of China. 相似文献
80.
Michael Pang 《Journal of Mathematical Analysis and Applications》2008,345(1):485-499
We extend the results obtained earlier in a joint paper with R. Banuelos, on the stability and approximations of the second Neumann eigenvalue and its corresponding eigenfunction, to the case when the second Neumann eigenvalue has multiplicity at least 2. We then show that our stability result can be applied to the Koch snowflake and the usual sequence of polygons approximating it from inside. 相似文献