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1.
A fast Cholesky decomposition and a fast inverse Cholesky decomposition method forA
T
A are presented, whereA is anm×n rectangular Toeplitz-block matrix, we give the FCD-algorithm for computingR, and the FICD-algorithm for computingR
−1, both allow for an efficient parallel implementation, for solving a least-squares problem and require onlyO(mn) operations.
Supported by the National Natural Science Foundation of China and NCP of China
Fang Yunlan: born in Aug. 1970, Past graduate student 相似文献
2.
A fast Cholesky factorization algorithm based on the classical Schur algorithm for themp×mp symmetric positive definite (s. p. d) block-Toeplitz matrices is presented. The relation between the generator and the Schur
complement of the matrices is explored. Besides, by applying the hyperbolic Householder transformations, we can reach an improved
algorithm whose computational complexity is2p
2m3−4pm3+3/2m3+O(pm).
Foundation item: Supported by the Natural Science Foundation of Hubei province
Biography: ZHANG Li(1973-), Female, MS, Research interests is in numerical algebra. 相似文献
3.
4.
Let dμ=ϕdν be a complex valued measure where ν is a non-negative measure and ϕ is a complex valued function which satisfiesb
p
+
orb
∞
+
⊂a
1 condition. We prove some basic martingale inequalities such as B-G inequalities, weak (p, p) and strong (p, p) type inequalities for Banach space valued martingale with respect to complex measure μ.
Supported by the National Natural Science Foundation of China
Hou Youliang: born in 1956, Ph. D 相似文献
5.
LetA bem byn matrix,M andN be positive definite matrices of orderm andn respectively. This paper presents an efficient method for computing (M?N) singular value decomposition ((M?N) SVD) ofA on a cube connected single instruction stream-multiple data stream (SIMD) parallel computer. This method is based on a one-sided orthogonalization algorithm due to Hestenes. On the cube connected SIMD parallel computer witho(n) processors, the (M?N)SVD of a matrixA requires a computation time ofo(m 3logm/n). 相似文献
6.
Zhu Fuliu 《武汉大学学报:自然科学英文版》1997,2(4):394-404
We study the Radon transform on the Cartan motion group associated with the bounded symmetric domainSO
* (8)/U(4), and prove that certain orbit of the regular elements is not the spectral synthesis set for the Fourier algebra on this
Cartan motion group.
Supported by the National Natural Science Foundation of China
Zhu Fuliu: born in Feb. 1945, Professor 相似文献
7.
In this paper, we prove an extrapolation theorem of operators in martingale spaces with A
p
weights, which shows that for operators T defined on martingale space L
u
1
, if T is bounded on martingale space L
p0(w) for some 1 < p
0 < ∞ and every, w∈ A
∞, so it is on L
p,s
(w) for every 1 < p, s < ∞, and w ∈ A
∞. We also get some properties of A
p
weights and prove that if w ∈ A
1, then the maximal operator M is bounded on L
p,q
(w) with 1 < p < ∞, 1 < q ≤ ∞. 相似文献
8.
YANG Qinqin~ FAN Yun~ . School of Mathematics Statistics Wuhan University Wuhan Hubei China . School of Mathematics Statistics Central China Normal University Wuhan Hubei China 《武汉大学学报:自然科学英文版》2006,11(3):469-472
0 IntroductionLeRte(f K.[,1]O), ,ki) .e b.e, aOips- am ocdoumlaplre tseys dtiesmcre(tese eva lCuhatpito .nII Iri nignwith unique maxi mal idealJ(O) suchthatJ(O) =(π)forπ∈O,Kis the quotient field ofOcharacteristic 0 ,andkis theresidue fieldO/(π)of characteristicp, wherepis a fixedpri me number .Inthis paper , we fix a finite groupG,andletKcontains all the |G|-throots of unity,where |G|is the or-der of finite groupG.In particular bothKandkare splittingfields of every subgroup ofG.D… 相似文献
9.
Denoted by M(A), QM(A) and SQM(A) the sets of all measures, quantum measures and subadditive quantum measures on a σ-algebra A, respectively. We observe that these sets are all positive cones in the real vector space F(A) of all real-valued functions on A and prove that M(A) is a face of SQM(A). It is proved that the product of m grade-1 measures is a grade-m measure. By combining a matrix M
μ to a quantum measure μ on the power set A
n
of an n-element set X, it is proved that μ ≪ ν (resp. μ ⊥ ν) if and only if M
μ ≪ M
ν
(resp. M
μ
M
ν
=0). Also, it is shown that two nontrivial measures μ and ν are mutually absolutely continuous if and only if μ·ν∈QM(A
n
). Moreover, the matrices corresponding to quantum measures are characterized. Finally, convergence of a sequence of quantum
measures on A
n
is introduced and discussed; especially, the Vitali-Hahn-Saks theorem for quantum measures is proved. 相似文献
10.
It is known that any strict tensor category (C,⊗,I) can determine a strict braided tensor categoryZ(C), the centre ofC. WhenA is a finite Hopf algebra, Drinfel’d has proved thatZ(
AM) is equivalent toD(A)M as a braided tensor category, whereAM is the left A-module category, andD(A) is the Drinfel’d double ofA. This is the categorical interpretation ofD(A). Z(
AM) is proved to be equivalent to the Yetter-Drinfel’d module category,AYD
A as a braided tensor category for any Hopf algebraA. Furthermore, for right A-comodule categoryM
A, Z(MA) is proved to be equivalent to the Yetter-Drinfel’d module categoryAY DA as a braided tensor category. But,in the two cases, the Yetter-Drinfel’d module categoryAY DA has different braided tensor structures. 相似文献
11.
再谈初等变换法在矩阵计算中的应用 总被引:2,自引:2,他引:0
冯天祥 《重庆三峡学院学报》2008,24(3):61-63
求矩阵的特征值和将一个矩阵对角化是矩阵计算中的重要任务之一,矩阵的QR分解更是矩阵计算的一种工具,但是这些过程都非常复杂.这里给出将矩阵对角化及求矩阵的QR分解式的初等变换法,同时给出了实现分解的算法,最后利用矩阵的三角分解式求QR分解式. 相似文献
12.
The R- and AR-indices: Complementing the h-index 总被引:47,自引:0,他引:47
JIN BiHui LIANG LiMing Ronald ROUSSEAU Leo EGGHE 《科学通报(英文版)》2007,52(6):855-863
Based on the foundation laid by the h-index we introduce and study the R- and AR-indices. These new indices eliminate some of the disadvantages of the h-index, especially when they are used in combina-tion with the h-index. The R-index measures the h-core’s citation intensity, while AR goes one step further and takes the age of publications into account. This allows for an index that can actually in-crease and decrease over time. We propose the pair (h, AR) as a meaningful indicator for research evaluation. We further prove a relation characterizing the h-index in the power law model. 相似文献
13.
We studied the problem of existence of jointly continuous local time for an additive process.Here, “local time” is understood in the sence of occupation density, and by an additive Lévy process we mean a process X={X(t), t∈Rd+)} which has the decomposition X= X1 X2 … XN. We prove that if the product of it slower index and N is greater than d, then a jointly continuous local time can be obtained via Berman's method. 相似文献
14.
举反例说明:对于矩阵的2-范数,存在矩阵A,B和C,使得A†CB†不是矩阵方程AXB-C=0的最佳逼近解,其中A†和B†分别是A和B的Moore-Penrose逆. 相似文献
15.
The Pólya conjecture and its connection with the weak Weyl-Berry conjecture are studied Specifically let Ω⊆R
n
(n≥1) be a non-empty bounded open set with boundary ∂Ω. LetN
0(λ, −Δ,Ω) be the Dirichlet counting function and φ(λ) the associated Weyl term. If the interior Minkowski dimension of ∂Ω
is δ∈[n−1,n], then under certain realisable conditions we prove that for λ sufficiently large the Pólya conjecture φ(λ) −N
0(λ,−Δ,Ω)≥0 is true. Under related conditions we also prove thatϕ(λ)−N
0(λ,−Δ, Ω)≈λ5/2, as λ→+∞. That is, the Weak Weyl-Berry conjecture is true. Similar results are obtained for the Neumann counting function.
Partially supported by the National Natural Science Foundation of China and the Royal Society of London
Chen Hua: born in March 8, 1956, Professor 相似文献
16.
ZhengShui-cao HuDi-he 《武汉大学学报:自然科学英文版》2004,9(3):269-272
We investigated the directed graph self similar sets under some weak overlapping condition. We get the multifractal decomposition formulas for these sets, i. e.,dim Ku^a DimKu^a =f(a), where fis the multifractal spectral function of the directed graph self similar measure. Especially, the results improve that of Edgar and Mauldin to the case which allows certain overlapping. 相似文献
17.
We demonstrate both theoretically and numerically that slow light can enhance the parametric process of silicon in photonic crystal line-defect waveguides. Specifically, to get the desired gain, the pump power for a given gain medium length or the gain medium length for given pump power can be reduced by (c/vgn)^2 when slow light waveguides are used, where n is the material index of conventional waveguide, vg is the group velocity of the slow light waveguide and c is the light velocity in vacuum. 相似文献
18.
Let C be a free cyclic code over Z
n
α and dim
p
C = k. In the paper, we prove that if the k characteristic generators of C are p-linearly independent then the corresponding nα − k characteristic generators of C
⊥ are p-linearly independent. We then show that to any trellis that can be constructed from k p-linearly independent characteristic generators of C, there exists a trellis for C
⊥ with the same state-complexity profile, which generalizes the conjecture of Koetter and Vardy to a free cyclic code over
Z
n
α.
Foundation item: Supported by the National Natural Science Foundation of China(60673071) 相似文献
19.
在前人研究的基础上,对块数为m×n、阶数为m r×ns的块-Toep litz矩阵T提出利用推广的Schur算法,通过对TTT的位移结构表示并结合Hyperbolic Householder变换对生成子矩阵作用,得到QR分解中上三角矩阵R的一种快速算法.在工程应用中采用一定近似,计算量可以达到O(ns3),较传统的Schur算法的计算量大大减小. 相似文献
20.
Zhang Yiping 《武汉大学学报:自然科学英文版》1997,2(1):30-34
Let Ω⊄R
d
and ξ∈∂Ω. LetE be any non-tangential subset of Ω. we prove that ifE is internal thin at ξ, then it is minimal thin at any minimal Martin boundary point of Ω.
Supported by the National Natural Science Foundation of China
Zhang Yiping: born in Dec. 1962. Professor 相似文献