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41.
蒋忠樟 《数学的实践与认识》2007,37(15):174-179
实对称正定矩阵的复合矩阵正定性的研究已有结论,但对于一般意义下的正定矩阵的复合矩阵是否仍然是正定的研究需要利用一般的正定矩阵的标准形的复合矩阵进行讨论,给出了一般公式及具体算法,为讨论其复合矩阵的正定性提供了基础条件. 相似文献
42.
S. Juneja 《Queueing Systems》2007,57(2-3):115-127
Efficient estimation of tail probabilities involving heavy tailed random variables is amongst the most challenging problems
in Monte-Carlo simulation. In the last few years, applied probabilists have achieved considerable success in developing efficient
algorithms for some such simple but fundamental tail probabilities. Usually, unbiased importance sampling estimators of such
tail probabilities are developed and it is proved that these estimators are asymptotically efficient or even possess the desirable
bounded relative error property. In this paper, as an illustration, we consider a simple tail probability involving geometric
sums of heavy tailed random variables. This is useful in estimating the probability of large delays in M/G/1 queues. In this setting we develop an unbiased estimator whose relative error decreases to zero asymptotically. The key
idea is to decompose the probability of interest into a known dominant component and an unknown small component. Simulation
then focuses on estimating the latter ‘residual’ probability. Here we show that the existing conditioning methods or importance
sampling methods are not effective in estimating the residual probability while an appropriate combination of the two estimates
it with bounded relative error. As a further illustration of the proposed ideas, we apply them to develop an estimator for
the probability of large delays in stochastic activity networks that has an asymptotically zero relative error.
相似文献
43.
Arne Barinka Stephan Dahlke Wolfgang Dahmen 《Advances in Computational Mathematics》2006,24(1-4):5-34
Recently adaptive wavelet methods have been developed which can be shown to exhibit an asymptotically optimal accuracy/work
balance for a wide class of variational problems including classical elliptic boundary value problems, boundary integral equations
as well as certain classes of noncoercive problems such as saddle point problems. A core ingredient of these schemes is the
approximate application of the involved operators in standard wavelet representation. Optimal computational complexity could
be shown under the assumption that the entries in properly compressed standard representations are known or computable in
average at unit cost. In this paper we propose concrete computational strategies and show under which circumstances this assumption
is justified in the context of elliptic boundary value problems.
Dedicated to Charles A. Micchelli on the occasion of his 60th birthday
Mathematics subject classifications (2000) 41A25, 41A46, 65F99, 65N12, 65N55.
This work has been supported in part by the Deutsche Forschungsgemeinschaft SFB 401, the first and third author are supported
in part by the European Community's Human Potential Programme under contract HPRN-CT-202-00286 (BREAKING COMPLEXITY). The
second author acknowledges the financial support provided through the European Union's Human Potential Programme, under contract
HPRN-CT-2002-00285 (HASSIP) and through DFG grant DA 360/4–1. 相似文献
44.
对称正交反对称矩阵反问题解存在的条件 总被引:25,自引:1,他引:24
戴华 《高等学校计算数学学报》2002,24(2):169-178
矩阵反问题和矩阵特征值反问题在科学和工程技术中具有广泛的应用,有关它们的研究已取得了许多进展[1,2].[3]和[4]分别研究了反对称矩阵反问题和双反对称矩阵特征值反问题等.本文研究一类更广泛的对称正交反对称矩阵反问题.用Rn×m(Cn×m)表示n×m实(复)矩阵的全体,ASRn×n表示n阶反对称矩阵的全体,ABSRn×n表示n阶双反对称矩阵的全体,ORn×n表示n阶正交矩阵的全体.A+表示矩阵A的Moore-Penrose广义逆.In表示n阶单位矩阵.ei表示n阶单位矩阵的第i列,Sn=[en,en-1, 相似文献
45.
S. M. Arabei D. V. Novik T. A. Pavich K. N. Solov’ev 《Journal of Applied Spectroscopy》2006,73(4):511-521
We have studied the fluorescence and fluorescence excitation spectra at 300 K, 77 K, and 4.2 K for silicate gel matrices colored
with meso-tetrapropylporphin by impregnation of the matrix with a solution of the pigment. Comparison of the data obtained
with the absorption spectra in acidified solutions and analysis of the low-temperature fine-structure vibronic spectra, and
also taking into account data obtained earlier for octaethylporphin in a xerogel showed formation of two cationic forms of
meso-tetrapropylporphin in the gel matrix: the short-wavelength form has a dicationic structure, while the long-wavelength form
has a monocationic structure. We have traced out the correlations of the vibrational structure in the spectra of the dicationic
form with data for the porphin dication, and we have drawn a number of conclusions concerning the normal vibrational modes
that are active in the vibronic fluorescence and absorption spectra of the studied cationic forms. Using the AM1 semiempirical
quantum chemical method, we optimized the geometry of the mesotetrapropylporphin dication: the most stable of the possible
conformers is the dication structure with saddleshaped macrocycle nonplanarity.
__________
Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 4, pp. 453–461, July–August, 2006. 相似文献
46.
Yongge Tian 《Journal of Mathematical Analysis and Applications》2002,266(2):333-341
We present an alternative expression for the parallel sum of k Hermitian nonnegative definite matrices by using the Moore-Penrose inverse of a block matrix. 相似文献
47.
48.
CHENDAOQI 《高校应用数学学报(英文版)》1994,9(1):35-43
In this paper, the normative matrices and their double LR transformation with origin shifts are defined, and the essential relationship between the double LR transformation of a normative matrix and the QR transformation of the related symmetric tridiagonal matrix is proved. We obtain a stable double LR algorithm for double LR transformation of normative matrices and give the error analysis of our algorithm. The operation number of the stable double LR algorithm for normative matrices is only four sevenths of the rational QR algorithm for reed symmetric tridiagonal matrices. 相似文献
49.
TAN Xiaojiang 《数学年刊B辑(英文版)》2002,23(4):531-538
Lei X be an arbitrary smooth irreducible complex projective curve, E (?) X a rank two vector bundle generated by its sections. The author first represents E as a triple {D1,D2,f}, where D1 , D2 are two effective divisors with d = deg(D1) + deg(D2), and f ∈ H0(X, [D1] |D2) is a collection of polynomials. E is the extension of [D2] by [D1] which is determined by f. By using f and the Brill-Noether matrix of D1 + D2, the author constructs a 2g X d matrix WE whose zero space gives Im{H0(X,[D1]) (?) H0(X, [D1] |D1)}(?)Im{H0(X, E) (?) H0(X,[D2]) (?) H0(X,[D2] |D2)}. From this and H0(X,E) = H0(X, [D1]) (?) Im{H0(X, E) (?) H0(X, [D2])}, it is got in particular that dimH0(X, E) = deg(E) - rank(WE) + 2. 相似文献
50.
设 G=(A,△)为紧矩阵量子群,G为A的所有有限维光滑的、不可约余表示等价类的集合.本文通过(A,△)的一个余表示Vo构造了两个相互配对的集合,利用Hilbert C*-模的理论证明它们分别为A和Baaj与Skandalis构造的量子群A,并且证明了对任意的α∈G,在A中都对应一个有限维投影算子Pα,满足 dim(α)=dim(pα). 相似文献