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1.
In this paper the accuracy of LU factorization of tridiagonal matrices without pivoting is considered. Two types of componentwise condition numbers for the L and U factors of tridiadonal matrices are presented and compared. One type is a condition number with respect to small relative perturbations of each entry of the matrix. The other type is a condition number with respect to small componentwise perturbations of the kind appearing in the backward error analysis of the usual algorithm for the LU factorization. We show that both condition numbers are of similar magnitude. This means that the algorithm is componentwise forward stable, i.e., the forward errors are of similar magnitude to those produced by a componentwise backward stable method. Moreover the presented condition numbers can be computed in O(n) flops, which allows to estimate with low cost the forward errors. AMS subject classification (2000) 65F35, 65F50, 15A12, 15A23, 65G50.Received October 2003. Accepted August 2004. Communicated by Per Christian Hansen.Froilán M. Dopico: This research has been partially supported by the Ministerio de Ciencia y Tecnología of Spain through grants BFM2003-06335-C03-02 (M. I. Bueno) and BFM2000-0008 (F. M. Dopico).  相似文献   

2.
Gromov Hyperbolicity of Riemann Surfaces   总被引:1,自引:0,他引:1  
We study the hyperbolicity in the Gromov sense of Riemann surfaces. We deduce the hyperbolicity of a surface from the hyperbolicity of its "building block components". We also prove the equivalence between the hyperbolicity of a Riemann surface and the hyperbolicity of some graph associated with it. These results clarify how the decomposition of a Riemann surface into Y-pieces and funnels affects the hyperbolicity of the surface. The results simplify the topology of the surface and allow us to obtain global results from local information.  相似文献   

3.
We study the existence of solution for nonlinear problems at resonance under Dirichlet boundary conditions. We deal with PDE's as well as systems of ODE's. The nonlinear terms considered are periodic functions: in particular, the problem is strongly resonant at infinity. By means of variational methods, we prove nondegeneracy under some hypotheses on the nonlinearities. Received: 31 October 2003, Accepted: 12 July 2004, Published online: 8 February 2005 Mathematics Subject Classification (2000): 34B15, 35B34, 35J20 The authors have been supported by the Ministry of Science and Technology of Spain (BFM2002-02649), and by J. Andalucía (FQM 116)  相似文献   

4.
Stochastic evolutional equations with monotone operators are considered in Banach spaces. Explicit and implicit numerical schemes are presented. The convergence of the approximations to the solution of the equations is proved. Mathematics Subject Classifications (2000) Primary: 60H15; Secondary: 65M60.István Gyöngy: This paper was written while the first named author was visiting the University of Paris X. The research of this author is partially supported by EU Network HARP.Annie Millet: The research of the second named author is partially supported by the research project BMF2003-01345.  相似文献   

5.
6.
We develop a primal-dual simplex algorithm for multicriteria linear programming. It is based on the scalarization theorem of Pareto optimal solutions of multicriteria linear programs and the single objective primal-dual simplex algorithm. We illustrate the algorithm by an example, present some numerical results, give some further details on special cases and point out future research. The paper was written during a visit of the first author to the University of Sevilla financed by a grant of the Andalusian Consejería de Educación. The research of the first author was partially supported by University of Auckland Grant 3602178/9275. The research of the second and third authors was partially financed by Spanish Grants BFM2001-2378, BFM2001-4028, MTM2004-0909 and HA2003-0121. We thank Anthony Przybylski for the implementation and making his results available. We thank the anonymous referees, whose comments have helped us to improve the presentation of the paper.  相似文献   

7.
The Cramér–Wold theorem states that a Borel probability measure P on ℝ d is uniquely determined by its one-dimensional projections. We prove a sharp form of this result, addressing the problem of how large a subset of these projections is really needed to determine P. We also consider extensions of our results to measures on a separable Hilbert space. First author partially supported by the Spanish Ministerio de Ciencia y Tecnología, grant BFM2002-04430-C02-02. Second author partially supported by Instituto de Cooperación Iberoamericana, Programa de Cooperación Interuniversitaria AL-E 2003. Third author partially supported by grants from NSERC and the Canada research chairs program.  相似文献   

8.
We provide second-order necessary and sufficient conditions for a point to be an efficient element of a set with respect to a cone in a normed space, so that there is only a small gap between necessary and sufficient conditions. To this aim, we use the common second-order tangent set and the asymptotic second-order cone utilized by Penot. As an application we establish second-order necessary conditions for a point to be a solution of a vector optimization problem with an arbitrary feasible set and a twice Fréchet differentiable objective function between two normed spaces. We also establish second-order sufficient conditions when the initial space is finite-dimensional so that there is no gap with necessary conditions. Lagrange multiplier rules are also given. This research was partially supported by Ministerio de Ciencia y Tecnología (Spain), Project BFM2003-02194. Online publication 29 January 2004.  相似文献   

9.
We study some geometrical properties associated to the contacts of surfaces with hyperhorospheres inH + 4 (−1). We introduce the concepts of osculating hyperhorospheres, horobinormals, horoasymptotic directions and horospherical points and provide conditions ensuring their existence. We show that totally semiumbilical surfaces have orthogonal horoasymptotic directions. Work partially supported by Grant-in-Aid for Scientific Research, JSPS, No. 12874007. Work partially supported by Grant-in-Aid for Scientific Research, JSPS, No. 12000266. Work partially supported by DGCYT grant no. BFM2003-02037.  相似文献   

10.
In this paper, we deal with the determination of the entire set of Pareto solutions of location problems involving Q general criteria. These criteria include median, center, or centdian objective functions as particular instances. We characterize the set of Pareto solutions of all these multicriteria problems for any polyhedral gauge. An efficient algorithm is developed for the planar case and its complexity is established. Extensions to the nonconvex case are also considered. The proposed approach is more general than previously published approaches to multicriteria location problems.The research of the third and fourth authors was partially supported by Grants BFM2001-2378, BFM2001-4028, BFM2004-0909, and HA2003-0121.  相似文献   

11.
Summary. This paper introduces a scheme for the numerical solution of a model for two turbulent flows with coupling at an interface. We consider a variational formulation of the coupled model, where the turbulent kinetic energy equation is formulated by transposition. We prove the convergence of the approximation to this formulation for 2D flows by piecewise affine triangular elements. Our main contribution is to prove that the standard Galerkin - finite element approximation of the Laplace equation approximates in L2 norm its solution by transposition, for data with low smoothness. We include some numerical tests for simple geometries that exhibit the behaviour predicted by our analysis.Mathematics Subject Classification (2000): 65 N30, 76M10Revised version received March 24, 2003This research was partially supported by Spanish Government REN2000-1162-C02-01 and REN2000-1168-C02-01 grants  相似文献   

12.
We introduce the notion of horospherical ridges for submanifolds of codimension 2 in hyperbolic n-space, and study some of their properties.*Work partially supported by DGCYT grant no. BFM2003-02037.  相似文献   

13.
The ground-breaking research on the uniformization of curves was conducted at the beginning of the last century. Nevertheless, there are few examples in the literature of algebraic curves for which an explicit uniformization is known. In this article we obtain an explicit uniformization of the Fermat curves F N , for each . The results presented here are based in part on an earlier study of the second author [6] in which each Riemann surface F N () was described as a quotient of the complex disk by a Fuchsian group Γ. 2000 Mathematics Subject Classification Primary—11F03, 11F06; Secondary—11F30 This work was partially supported by MCYT BFM2000-0627 and BMF2003-01898.  相似文献   

14.
A useful characterization of the cone of attainable directions is provided.This research was partially supported by the Ministerio de Ciencia y Tecnología (Spain), Project BFM2003-02194.  相似文献   

15.
We prove the existence and uniqueness of solution for a first-order ordinary differential equation with periodic boundary conditions admitting only the existence of a lower solution. To this aim, we prove an appropriate fixed point theorem in partially ordered sets. ★ Partially supported by Ministerio de Ciencia y Tecnología/ FEDER, project BFM2001-3884-C02-01; and by Xunta de Galicia/ FEDER, project PGIDIT02PXIC20703PN.  相似文献   

16.
The paper presents a sensitivity analysis of Pareto solutions on the basis of the Karush-Kuhn-Tucker (KKT) necessary conditions applied to nonlinear multiobjective programs (MOP) continuously depending on a parameter. Since the KKT conditions are of the first order, the sensitivity properties are considered in the first approximation. An analogue of the shadow prices, well known for scalar linear programs, is obtained for nonlinear MOPs. Two types of sensitivity are investigated: sensitivity in the state space (on the Pareto set) and sensitivity in the cost function space (on the balance set) for a vector cost function. The results obtained can be used in applications for sensitivity computation under small variations of parameters. Illustrative examples are presented.Research of this author was partially supported by Grant BEC2003-09067-C04-03.Research of this author was partially supported by NSERC Grant RGPIN-3492-00.Research of this author was partially supported by Grant BEC2003-09067-C04-02.  相似文献   

17.
In this paper we deal with the ordered median problem: a family of location problems that allows us to deal with a large number of real situations which does not fit into the standard models of location analysis. Moreover, this family includes as particular instances many of the classical location models. Here, we analyze thep-facility version of this problem on networks and our goal is to study the structure of the set of candidate points to be optimal solutions. The research of the authors is partially financed by Spanish research grants BFM2001-2378, BFM2001-4028, BFM2004-0909 and HA2003-0121.  相似文献   

18.
In this paper we address bargaining games where the agents have to take into account different criteria to value the decisions. We propose the class of generalized maximin solutions, as the natural extension for these games of the maximin solutions in conventional bargaining. In order to refine this solution concept, we define a multicriteria lexicographic partial ordering and present the class of generalized leximin solutions as those that are nondominated with respect to this relation. We establish some properties of these solutions and characterize them as solutions of multicriteria problems. The research of the authors is partially supported by the Spanish Ministry of Science and Technology projects BFM2002-11282-E and BEC2003-03111.  相似文献   

19.
We define the relative mean curvature directions on surfaces immersed in ℝn, n ≥ 4, generalizing the concept of mean curvature directions for surfaces in 4-space studied by Mello. We obtain their differential equations and study their corresponding generic configurations. *Work partially supported by DGCYT grant no. MTM2004-03244 and Unimontes-BR. †Work partially supported by DGCYT grant no. MTM2004-03244. ‡Work partially supported by DGCYT grant no. BFM2003-0203.  相似文献   

20.
On CL-spaces and almost CL-spaces   总被引:3,自引:0,他引:3  
We find some necessary conditions for a real Banach space to be an almost CL-space. We also discuss the stability of CL-spaces and almost CL-spaces byc 0- andl 1-sums. Finally, we address the question if a space of vector-valued continuous functions can be a CL-space or an almost CL-space. Research partially supported by Spanish MCYT project no. BFM2000-1467.  相似文献   

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