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991.
992.
A truncated ULV decomposition (TULVD) of an m×n matrix X of rank k is a decomposition of the form X = ULVT+E, where U and V are left orthogonal matrices, L is a k×k non‐singular lower triangular matrix, and E is an error matrix. Only U,V, L, and ∥E∥F are stored, but E is not stored. We propose algorithms for updating and downdating the TULVD. To construct these modification algorithms, we also use a refinement algorithm based upon that in (SIAM J. Matrix Anal. Appl. 2005; 27 (1):198–211) that reduces ∥E∥F, detects rank degeneracy, corrects it, and sharpens the approximation. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
993.
A decomposition ??={G1, G2,…,Gs} of a graph G is a partition of the edge set of G into edge‐disjoint subgraphs G1, G2,…,Gs. If Gi?H for all i∈{1, 2, …, s}, then ?? is a decomposition of G by H. Two decompositions ??={G1, G2, …, Gn} and ?={F1, F2,…,Fn} of the complete bipartite graph Kn,n are orthogonal if |E(Gi)∩E(Fj)|=1 for all i,j∈{1, 2, …, n}. A set of decompositions {??1, ??2, …, ??k} of Kn, n is a set of k mutually orthogonal graph squares (MOGS) if ??i and ??j are orthogonal for all i, j∈{1, 2, …, k} and i≠j. For any bipartite graph G with n edges, N(n, G) denotes the maximum number k in a largest possible set {??1, ??2, …, ??k} of MOGS of Kn, n by G. El‐Shanawany conjectured that if p is a prime number, then N(p, Pp+ 1)=p, where Pp+ 1 is the path on p+ 1 vertices. In this article, we prove this conjecture. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 369–373, 2009 相似文献
994.
Thomas Führer Michael Karkulik 《Numerical Methods for Partial Differential Equations》2019,35(5):1777-1800
We provide new insights into the a priori theory for a time‐stepping scheme based on least‐squares finite element methods for parabolic first‐order systems. The elliptic part of the problem is of general reaction‐convection‐diffusion type. The new ingredient in the analysis is an elliptic projection operator defined via a nonsymmetric bilinear form, although the main bilinear form corresponding to the least‐squares functional is symmetric. This new operator allows to prove optimal error estimates in the natural norm associated to the problem and, under additional regularity assumptions, in the L2 norm. Numerical experiments are presented which confirm our theoretical findings. 相似文献
995.
采用盐酸为介质,以顺序注射-氢化物发生原子荧光法测定生产用水中的锑含量.通过正交实验确定了仪器工作参数,研究了介质浓度、KBH4浓度、硫脲一抗坏血酸加入量等因素对测定结果的影响,探讨了共存离子的干扰.在选定的最佳实验条件下,方法的检出限为0.011ng/mL,线性范围0~8ng/mL,相对标准偏差为2.78%~6.20%,加标回收率为91.0%~99.1%.该方法操作简便,灵敏度高,准确度好,与微波消解法相比较,两者无显著性差异. 相似文献
996.
997.
John T. Conway 《Integral Transforms and Special Functions》2019,30(3):166-180
A method is presented for deriving integrals of special functions which obey inhomogeneous second-order linear differential equations. Inhomogeneous equations are readily derived for functions satisfying second-order homogeneous equations. Sample results are derived for Bessel functions, parabolic cylinder functions, Gauss hypergeometric functions and the six classical orthogonal polynomials. For the orthogonal polynomials the method gives indefinite integrals which reduce to the usual orthogonality conditions on the usual orthogonality intervals. These indefinite integrals for the orthogonal polynomials appear to be new. All results have been checked with Mathematica. 相似文献
998.
In this paper, we present a new method for frequency domain identification of discrete linear time‐invariant systems. We take consideration of the case where the output noises are mixed or unknown. In order to deal with this problem, a new mixed model structure is used correspondingly. The augmented Lagrangian method (ALM) is combined in selection of poles for the shifted Cauchy kernels to get solutions to the optimal problem. Simulations show the proposed method can get efficient approximation to the original systems. 相似文献
999.
Orthogonal decomposition of the special linear Lie algebra over the complex numbers was studied in the early 1980s and attracted further attentions in the past decade due to its application in quantum information theory. In this paper, we study this decomposition problem of the special linear Lie algebra over a finite commutative ring with identity. 相似文献
1000.
This paper addresses the numerical modeling of the solidification of a binary alloy that obeys a liquidus–solidus phase diagram. In order to capture the moving melting front, we introduce a Lagrange projection scheme based on a random sampling projection. Using a finite volume formulation, we define accurate numerical fluxes for the temperature and concentration fields which guarantee the sharp treatment of the boundary conditions at the moving front, especially the jump of the concentration according to the liquidus–solidus diagram. We provide some numerical illustrations which assess the good behavior of the method: maximum principle, stability under CFL condition, numerical convergence toward self‐similar solutions, ability to handle two melting fronts. 相似文献