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1.
In this paper, we will propose algorithms for calculating a minimal ellipsoid circumscribing a polytope defined by a system
of linear inequalities. If we know all vertices of the polytope and its cardinality is not very large, we can solve the problem
in an efficient manner by a number of existent algorithms. However, when the polytope is defined by linear inequalities, these
algorithms may not work since the cardinality of vertices may be huge. Based on a fact that vertices determining an ellipsoid
are only a fraction of these vertices, we propose algorithms which iteratively calculate an ellipsoid which covers a subset
of vertices. Numerical experiment shows that these algorithms perform well for polytopes of dimension up to seven. 相似文献
2.
Eva Lesanska 《Applications of Mathematics》2002,47(5):411-426
The problem is to determine nonsensitiveness regions for threshold ellipsoids within a regular mixed linear model. 相似文献
3.
Let f :X→X be a continuous map of a compact metric space to itself. We prove that f is topologically conjugate to an adding machine map if and only if X is an infinite minimal set for f and each point of X is regularly recurrent. Moreover, if X is an infinite minimal set for f and one point of X is regularly recurrent, then f is semiconjugate to an adding machine map. 相似文献
4.
对于那些由代数微分方程描述的具有输入输出关系的非线性控制系统,本文采用两种方法讨论了其最小实现问题:一种方法是直接计算系统的特征列;另一种方法则采用了本原元定理.两种方法给出的最小实现所需的状态变量最小数目是相等的.文中的大量代数与微分运算则可利用数学机械化来完成 相似文献
5.
Florin Ambro 《Central European Journal of Mathematics》2006,4(3):358-370
We describe the set of minimal log discrepancies of toric log varieties, and study its accumulation points.
This work is supported by a 21st Century COE Kyoto Mathematics Fellowship, and a JSPS Grant-in-Aid No 17740011. 相似文献
6.
Brian Lucena 《Discrete Applied Mathematics》2007,155(8):1055-1065
One consequence of the graph minor theorem is that for every k there exists a finite obstruction set Obs(TW?k). However, relatively little is known about these sets, and very few general obstructions are known. The ones that are known are the cliques, and graphs which are formed by removing a few edges from a clique. This paper gives several general constructions of minimal forbidden minors which are sparse in the sense that the ratio of the treewidth to the number of vertices n does not approach 1 as n approaches infinity. We accomplish this by a novel combination of using brambles to provide lower bounds and achievable sets to demonstrate upper bounds. Additionally, we determine the exact treewidth of other basic graph constructions which are not minimal forbidden minors. 相似文献
7.
The many facets of linear programming 总被引:1,自引:0,他引:1
Michael J. Todd 《Mathematical Programming》2002,91(3):417-436
We examine the history of linear programming from computational, geometric, and complexity points of view, looking at simplex,
ellipsoid, interior-point, and other methods.
Received: June 22, 2000 / Accepted: April 4, 2001?Published online October 2, 2001 相似文献
8.
Let Hn be an n-dimensional Haar subspace of
and let Hn−1 be a Haar subspace of Hn of dimension n−1. In this note we show (Theorem 6) that if the norm of a minimal projection from Hn onto Hn−1 is greater than 1, then this projection is an interpolating projection. This is a surprising result in comparison with Cheney and Morris (J. Reine Angew. Math. 270 (1974) 61 (see also (Lecture Notes in Mathematics, Vol. 1449, Springer, Berlin, Heilderberg, New York, 1990, Corollary III.2.12, p. 104) which shows that there is no interpolating minimal projection from C[a,b] onto the space of polynomials of degree n, (n2). Moreover, this minimal projection is unique (Theorem 9). In particular, Theorem 6 holds for polynomial spaces, generalizing a result of Prophet [(J. Approx. Theory 85 (1996) 27), Theorem 2.1]. 相似文献
9.
In this paper we establish the existence of the minimal large positive solution for a general class of nonlinear cooperative systems including the simplest prototype of García-Melián et al. (2016). Precisely, based on the existence of a large positive supersolution, we can infer the existence of the minimal large positive solution. Moreover, we also give some sufficient easily computable conditions for the existence of a large positive supersolution. Our results generalize, very substantially, some of the findings of García-Melián et al. (2016) adopting a rather novel methodology. 相似文献
10.
Marc Soret 《Annals of Global Analysis and Geometry》1995,13(2):101-116
The main result of this paper is the following maximum principle at infinity:Theorem.Let M
1
and M
2
be two disjoint properly embedded complete minimal surfaces with nonempty boundaries, that are stable in a complete flat 3-manifold. Then dist(M
1,M
2)=min(dist(M
1,M
2), dist(M
2,M
1)).In case one boundary is empty, e.g. M
1,then dist(M
1,M
2)=dist(M
2,M
1).If both boundaries are empty, then M
1
and M
2
are flat. 相似文献