共查询到20条相似文献,搜索用时 15 毫秒
1.
ZHANG YingShan LI WeiGuo MAO ShiSong & ZHENG ZhongGuo School of Finance Statistics East China Normal University Shanghai China School of Sciences Beijing University of Aeronautics Astronautics Beijing Lab of Mathematics Its Application Peking University Beijing 《中国科学 数学(英文版)》2011,(1)
Nowadays orthogonal arrays play important roles in statistics, computer science, coding theory and cryptography. The usual difference matrices are essential for the construction for many mixed orthogonal arrays. But there are also orthogonal arrays which cannot be obtained by the usual difference matrices, such as mixed orthogonal arrays of run size 60. In order to construct these mixed orthogonal arrays, a class of special so-called generalized difference matrices were discovered by Zhang (1989,1990,1993,2... 相似文献
2.
Nowadays orthogonal arrays play important roles in statistics,computer science, coding theory and cryptography.The usual difference matrices are essential for the con- struction of many mixed orthogonal arrays.But there are also many orthogonal arrays, especially mixed-level or asymmetrical which can not be obtained by the usual difference matrices.In order to construct these asymmetrical orthogonal arrays,a class of special matrices,so-called generalized difference matrices,were discovered by Zhang(1989,1990, 1993) by the orthogonal decompositions of projective matrices.In this article,an interesting equivalent relationship between the orthogonal arrays and the generalized difference matri- ces is presented.As an application,a family of orthogonal arrays of run sizes 4p~2,such as L_(36)(6~13~42~(10)),are constructed. 相似文献
3.
Nowadays orthogonal arrays play important roles in statistics, computer science, coding theory and cryptography. The usual difference matrices are essential for the construction of many mixed orthogonal arrays. But there are also many orthogonal arrays, especially mixed-level or asymmetrical which can not be obtained by the usual difference matrices. In order to construct these asymmetrical orthogonal arrays, a class of special matrices, so-called generalized difference matrices, were discovered by Zhang(1989, 1990, 1993) by the orthogonal decompositions of projective matrices. In this article, an interesting equivalent relationship between the orthogonal arrays and the generalized difference matrices is presented. As an application, a family of orthogonal arrays of run sizes 4p2, such as L36(6^13^42^10), are constructed. 相似文献
4.
Discrete wavelet transform approximation is an established means of approximating dense linear systems arising from discretization
of differential and integral equations defined on a one-dimensional domain. For higher dimensional problems, approximation
with a sum of Kronecker products has been shown to be effective in reducing storage and computational costs. We have combined
these two approaches to enable solution of very large dense linear systems by an iterative technique using a Kronecker product
approximation represented in a wavelet basis. Further approximation of the system using only a single Kronecker product provides
an effective preconditioner for the system. Here we present our methods and illustrate them with some numerical examples.
This technique has the potential for application in a range of areas including computational fluid dynamics, elasticity, lubrication
theory and electrostatics.
AMS subject classification 65F10, 65T60, 65F30
Judith M. Ford: This author was supported by EPSRC Postdoctoral Research Fellowship ref: GR/R95982/01. Current address: Royal
Liverpool Children's NHS Trust, Liverpool, L12 2AP.
Eugene E. Tyrtyshnikov: This author was supported by the Russian Fund of Basic Research (grant 02-01-00590) and Science Support
Foundation. 相似文献
5.
This paper considers the application of Kronecker product for the construction of factorial designs, with orthogonal factorial structure, in a set-up for multiway elimination of heterogeneity. A technique involving the use of projection operators has been employed to show how a control can be achieved over the interaction efficiencies. A modification of the ordinary Kronecker product yielding smaller designs has also been considered. The results appear to have a fairly wide coverage. 相似文献
6.
构造正交表的一种替换模式 总被引:1,自引:0,他引:1
A method of constructing orthogonal arrays is presented by Zhang, Lu and Pang in 1999. In this paper,the method is developed by introducing a replacement scheme on the construction of orthogonal arrays ,and some new mixed-level orthogonal arrays of run size 36 are constructed. 相似文献
7.
D. T. Todorov 《组合设计杂志》2012,20(8):363-367
The paper gives example of orthogonal array OA(6, 14) obtained from a difference matrix . The construction is equivalent to four mutually orthogonal Latin squares (MOLS) of order 14. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 20: 363–367, 2012 相似文献
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For a graph G, κ(G) denotes its connectivity. The Kronecker product G1×G2 of graphs G1 and G2 is the graph with the vertex set V(G1)×V(G2), two vertices (u1,v1) and (u2,v2) being adjacent in G1×G2 if and only if u1u2∈E(G1) and v1v2∈E(G2). Guji and Vumar [R. Guji, E. Vumar, A note on the connectivity of Kronecker products of graphs, Appl. Math. Lett. 22 (2009) 1360–1363] conjectured that for any nontrivial graph G, κ(G×Kn)=min{nκ(G),(n−1)δ(G)} when n≥3. In this note, we confirm this conjecture to be true. 相似文献
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Tatjana von Rosen 《Linear and Multilinear Algebra》2013,61(5):595-606
In this article, we derive explicit expressions for the entries of the inverse of a patterned matrix that is a sum of Kronecker products. This matrix keeps the Kronecker structure under matrix inversion, and it is used, for example, in statistics, in particular in the linear mixed model analysis. The obtained results present new and extended existing algorithms for the inversion of the considered patterned matrices. We also obtain a closed-form inverse in terms of block matrices. 相似文献
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The preconditioned iterative solvers for solving Sylvester tensor equations are considered in this paper.By fully exploiting the structure of the tensor equation,we propose a projection method based on the tensor format,which needs less flops and storage than the standard projection method.The structure of the coefficient matrices of the tensor equation is used to design the nearest Kronecker product(NKP) preconditioner,which is easy to construct and is able to accelerate the convergence of the iterative solver.Numerical experiments are presented to show good performance of the approaches. 相似文献
13.
We generalize the matrix Kronecker product to tensors and propose the tensor Kronecker product singular value decomposition that decomposes a real k‐way tensor into a linear combination of tensor Kronecker products with an arbitrary number of d factors. We show how to construct , where each factor is also a k‐way tensor, thus including matrices (k=2) as a special case. This problem is readily solved by reshaping and permuting into a d‐way tensor, followed by a orthogonal polyadic decomposition. Moreover, we introduce the new notion of general symmetric tensors (encompassing symmetric, persymmetric, centrosymmetric, Toeplitz and Hankel tensors, etc.) and prove that when is structured then its factors will also inherit this structure. 相似文献
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L. Elsner 《Linear algebra and its applications》2011,434(4):1058-1066
The well known bialternate product of two square matrices is re-examined together with another matrix product defined by means of the permanent function and having similar properties. Old and new results concerning both products are presented in a unified manner. A simple and elegant relation with the Kronecker product of matrices is also given. 相似文献
16.
Lisa Perrone 《Numerical Linear Algebra with Applications》2006,13(1):1-22
The anti‐reflective boundary condition for image restoration was recently introduced as a mathematically desirable alternative to other boundary conditions presently represented in the literature. It has been shown that, given a centrally symmetric point spread function (PSF), this boundary condition gives rise to a structured blurring matrix, a submatrix of which can be diagonalized by the discrete sine transform (DST), leading to an O(n2 log n) solution algorithm for an image of size n × n. In this paper, we obtain a Kronecker product approximation of the general structured blurring matrix that arises under this boundary condition, regardless of symmetry properties of the PSF. We then demonstrate the usefulness and efficiency of our approximation in an SVD‐based restoration algorithm, the computational cost of which would otherwise be prohibitive. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
17.
讨论了108次混合正交表,借助于计算机程序,将计算机搜索的方法应用于投影矩阵正交分解构造正交表的方法中,构造了一些新的混合正交表. 相似文献
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Mercedes H. Rosas 《Journal of Algebraic Combinatorics》2001,14(2):153-173
The Kronecker product of two Schur functions s
and s
, denoted by s
* s
, is the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group corresponding to the partitions and . The coefficient of s
in this product is denoted by
, and corresponds to the multiplicity of the irreducible character in .We use Sergeev's Formula for a Schur function of a difference of two alphabets and the comultiplication expansion for s
[XY] to find closed formulas for the Kronecker coefficients
when is an arbitrary shape and and are hook shapes or two-row shapes.Remmel (J.B. Remmel, J. Algebra
120 (1989), 100–118; Discrete Math.
99 (1992), 265–287) and Remmel and Whitehead (J.B. Remmel and T. Whitehead, Bull. Belg. Math. Soc. Simon Stiven
1 (1994), 649–683) derived some closed formulas for the Kronecker product of Schur functions indexed by two-row shapes or hook shapes using a different approach. We believe that the approach of this paper is more natural. The formulas obtained are simpler and reflect the symmetry of the Kronecker product. 相似文献
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