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91.
Simon R. Blackburn 《Journal of Combinatorial Theory, Series A》2006,113(7):1572-1581
The paper contains proofs of the following results. For all sufficiently large odd integers n, there exists a set of 2n−1 permutations that pairwise generate the symmetric group Sn. There is no set of 2n−1+1 permutations having this property. For all sufficiently large integers n with n≡2mod4, there exists a set of 2n−2 even permutations that pairwise generate the alternating group An. There is no set of 2n−2+1 permutations having this property. 相似文献
92.
A. A. Maleev 《Computational Mathematics and Mathematical Physics》2006,46(12):2031-2039
Stationary and nonstationary Jacobi-like iterative processes for solving systems of linear algebraic equations are examined. For a system whose coefficient matrix A is an H-matrix, it is shown that the convergence rate of any Jacobi-like process is at least as high as that of the point Jacobi method as applied to a system with 〈A〉 as the coefficient matrix, where 〈A〉 is a comparison matrix of A. 相似文献
93.
Covering numbers of precompact symmetric convex subsets of Hilbert spaces are investigated. Lower bounds are derived for sets containing orthogonal subsets with norms of their elements converging to zero sufficiently slowly. When these sets are convex hulls of sets with power-type covering numbers, the bounds are tight. The arguments exploit properties of generalized Hadamard matrices. The results are illustrated by examples from machine learning, neurocomputing, and nonlinear approximation. 相似文献
94.
This paper investigates the existence of positive solutions of a singular boundary value problem with negative exponent similar
to standard Emden-Fowler equation. A necessary and sufficient condition for the existence of C[0, 1] positive solutions as
well as C1[0, 1] positive solutions is given by means of the method of lower and upper solutions with the Schauder fixed point theorem. 相似文献
95.
Bing-sheng He Zhen-hua Yang Xiao-ming Yuan 《Journal of Mathematical Analysis and Applications》2004,300(2):139-374
Proximal point algorithms (PPA) are attractive methods for monotone variational inequalities. The approximate versions of PPA are more applicable in practice. A modified approximate proximal point algorithm (APPA) presented by Solodov and Svaiter [Math. Programming, Ser. B 88 (2000) 371–389] relaxes the inexactness criterion significantly. This paper presents an extended version of Solodov–Svaiter's APPA. Building the direction from current iterate to the new iterate obtained by Solodov–Svaiter's APPA, the proposed method improves the profit at each iteration by choosing the optimal step length along this direction. In addition, the inexactness restriction is relaxed further. Numerical example indicates the improvement of the proposed method. 相似文献
96.
Xian Xu 《Journal of Mathematical Analysis and Applications》2004,291(2):673-689
In this paper, some multiplicity results for positive solutions of some singular semi-positone three-point boundary value problem be obtained by using the fixed point index method. 相似文献
97.
Shunsuke Inenaga Ayumi Shinohara Masayuki Takeda Setsuo Arikawa 《Journal of Discrete Algorithms》2004,2(1):33
Suffix trees are a well-known and widely-studied data structure highly useful for string matching. The suffix tree of a string w can be constructed in O(n) time and space, where n denotes the length of w. Larsson achieved an efficient algorithm to maintain suffix trees for a sliding window. It contributes to prediction by partial matching (PPM) style statistical data compression scheme. Compact directed acyclic word graphs (CDAWGs) are a more space-economical data structure for indexing strings. In this paper we propose a linear-time algorithm to maintain CDAWGs for a sliding window. 相似文献
98.
Gabriela Jeronimo Teresa Krick Juan Sabia Martín Sombra 《Foundations of Computational Mathematics》2004,4(1):41-117
We present a bounded probability algorithm for the computation of the
Chowforms of the equidimensional components of an algebraic variety. In particular,
this gives an alternative procedure for the effective equidimensional decomposition
of the variety, since each equidimensional component is characterized by its Chow
form.
The expected complexity of the algorithm is polynomial in the size and the geometric
degree of the input equation system defining the variety. Hence it improves (or
meets in some special cases) the complexity of all previous algorithms for computing Chow forms. In addition to this, we clarify the probability and uniformity aspects,
which constitutes a further contribution of the paper.
The algorithm is based on elimination theory techniques, in line with the geometric
resolution algorithm due to M. Giusti, J. Heintz, L. M. Pardo, and their collaborators.
In fact, ours can be considered as an extension of their algorithm for zero-dimensional
systems to the case of positive-dimensional varieties. The key element for dealing
with positive-dimensional varieties is a new Poisson-type product formula. This
formula allows us to compute the Chow form of an equidimensional variety from a
suitable zero-dimensional fiber.
As an application, we obtain an algorithm to compute a subclass of sparse resultants,
whose complexity is polynomial in the dimension and the volume of the input
set of exponents. As another application, we derive an algorithm for the computation
of the (unique) solution of a generic overdetermined polynomial equation system. 相似文献
99.
Binary Decision Diagrams (BDDs) are the state-of-the-art data structure for representation and manipulation of Boolean functions. In general, exact BDD minimization is NP-complete. For BDD-based technology, a small improvement in the number of nodes often simplifies the follow-up problem tremendously. This paper proposes an elitism-based evolutionary algorithm (EBEA) for BDD minimization. It can efficiently find the optimal orderings of variables for all LGSynth91 benchmark circuits with a known minimum size. Moreover, we develop a distributed model of EBEA, DEBEA, which obtains the best-ever variable orders for almost all benchmarks in the LGSynth91. Experimental results show that DEBEA is able to achieve super-linear performance compared to EBEA for some hard benchmarks. 相似文献
100.
In this work, the NP-hard maximum clique problem on graphs is considered. Starting from basic greedy heuristics, modifications and improvements are proposed and combined in a two-phase heuristic procedure. In the first phase an improved greedy procedure is applied starting from each node of the graph; on the basis of the results of this phase a reduced subset of nodes is selected and an adaptive greedy algorithm is repeatedly started to build cliques around such nodes. In each restart the selection of nodes is biased by the maximal clique generated in the previous execution. Computational results are reported on the DIMACS benchmarks suite. Remarkably, the two-phase procedure successfully solves the difficult Brockington-Culberson instances, and is generally competitive with state-of-the-art much more complex heuristics. 相似文献