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91.
92.
Complex symmetric matrices often appear in quantum physics in the solution methods of partial differential equations such as the Schrödinger equation. We have recently introduced a new fast and efficient direct eigensolver for this problem in [4], and reported its performance in the eigenvalue calculation in [3]. In this paper, we further report on some benchmark tests for computing the full and partial eigenspectrum on a variety of super computing machines, i.e., the Cray J-932, the DEC Alfa 8400, and the SGI Power Challenge 8000 and 10000. We observe that in all cases the new algorithm is much faster than codes available in standard state of the art eigensolver packages such as LAPACK. 相似文献
93.
本文研究n阶实对称矩阵A的前m项最大特征值之和fm(A)的非光滑分析问题.利用Ky-Fan的关于特征值之和的变分原理以及凸分析理论,得到了fm(A)的次梯度和方向导数的显式表达式. 相似文献
94.
The nonsymmetric Lanczos method has recently received significant attention as a model reduction technique for large-scale systems. Unfortunately, the Lanczos method may produce an unstable partial realization for a given, stable system. To remedy this situation, unexpensive implicit restarts are developed which can be employed to stabilize the Lanczos generated model.This work was supported in part by ARPA (US Army ORA4466.01), by ARPA (Grant 60NANB2D1272), by the Department of Energy (Contract DE-FG0f-91ER25103) and by the National Science Foundation (Grants CCR-9209349 and CCR-9120008). 相似文献
95.
Solutions of the Fokker-Planck (Kramers) equation in position-velocity space for the double-well potentiald
2x2/2+d4x4/4 in terms of matrix continued fractions are derived. It is shown that the method is also applicable to a Boltzmann equation with a BGK collision operator. Results of eigenvalues and of the Fourier transform of correlation functions are presented explicitly. The lowest nonzero eigenvalue is compared with the escape rate in the weak noise limit for various damping constants and the susceptibility is compared with the zero-friction-limit result. 相似文献
96.
P.R. Krishnaiah 《Journal of multivariate analysis》1976,6(1):1-30
In this paper, the author gives a review of the literature on complex multivariate distributions. Some new results on these distributions are also given. Finally, the author discusses the applications of the complex multivariate distributions in the area of the inference on multiple time series. 相似文献
97.
《Journal of Computational and Applied Mathematics》1994,50(1-3):51-66
The paper deals with the finite-element analysis of second-order elliptic eigenvalue problems when the approximate domains Ωh are not subdomains of the original domain
. The considerations are restricted to piecewise linear approximations. Special attention is devoted to the convergence of approximate eigenfunctions in the case of multiple exact eigenvalues. As yet the approximate solutions have been compared with linear combinations of exact eigenfunctions with coefficients depending on the mesh parameter h. We avoid this disadvantage. 相似文献
98.
M R M Witwit 《Pramana》1994,42(4):333-340
The Schrödinger equation with the potentialV(r)=D[exp(?2β(r?r e))?2exp(?β(r?r e))] is treated in the framework of the hypervirial-renormalization parameter scheme. The energy eigenvalues of various eigenstates for different molecules are calculated. 相似文献
99.
Using an algebraic technique based on the Lie algebra of the group SO(2, 1) the eigenvalues of the triple-well anharmonic
oscillator are calculated for all ranges of the coupling constant. Approximate analytic formulas for the eigenvalues up to
second order are given. The results obtained are compared with those of other authors. 相似文献
100.