共查询到20条相似文献,搜索用时 125 毫秒
1.
Hoang Luc Nguyen Huy Tuan Nguyen Kirane Mokhtar Xuan Thanh Duong Dang 《Mathematical Methods in the Applied Sciences》2019,42(5):1561-1571
We investigate a backward problem for the Rayleigh‐Stokes problem, which aims to determine the initial status of some physical field such as temperature for slow diffusion from its present measurement data. This problem is well‐known to be ill‐posed because of the rapid decay of the forward process. We construct a regularized solution using the filter regularization method in the Gaussian random noise. Under some a priori assumptions on the exact solution, we establish the expectation between the exact solution and the regularized solution in the L2 and Hm norms. 相似文献
2.
We justify the application of the averaging method to optimal control problems for systems of differential equations on the
half-line. For optimal control problems for systems of differential equations linear in the control, we prove the existence
of optimal controls for the exact and averaged problems. We show that an optimal control in the averaged problem is ɛ-optimal in the exact problem. 相似文献
3.
Petros Drineas Michael W. Mahoney S. Muthukrishnan Tamás Sarlós 《Numerische Mathematik》2011,117(2):219-249
Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact
solution. In a typical setting, one lets n be the number of constraints and d be the number of variables, with n >> d{n \gg d}. Then, existing exact methods find a solution vector in O(nd
2) time. We present two randomized algorithms that provide accurate relative-error approximations to the optimal value and
the solution vector of a least squares approximation problem more rapidly than existing exact algorithms. Both of our algorithms
preprocess the data with the Randomized Hadamard transform. One then uniformly randomly samples constraints and solves the
smaller problem on those constraints, and the other performs a sparse random projection and solves the smaller problem on
those projected coordinates. In both cases, solving the smaller problem provides relative-error approximations, and, if n is sufficiently larger than d, the approximate solution can be computed in O(nd ln d) time. 相似文献
4.
M. Sh. Shabozov 《Ukrainian Mathematical Journal》2012,63(10):1633-1639
We consider the problem of finding exact inequalities for the best approximations of periodic differentiable functions by
trigonometric polynomials and the m-order moduli of continuity in the space L
2 and present their applications. For some classes of functions defined by the indicated moduli of continuity, we calculate
the exact values of n-widths in the space L
2. 相似文献
5.
Kab Seok Kang Do Young Kwak 《Numerical Methods for Partial Differential Equations》2006,22(1):165-179
We investigate an L2‐error estimate of a covolume scheme for the Stokes problem recently introduced by Chou (Math Comp 66 (1997), 85–104). We show the error in L2 norm is of second order provided the exact velocity is in H 3 and the exact pressure is in H2. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 相似文献
6.
Petrica C. Pop 《Journal of Mathematical Modelling and Algorithms》2004,3(2):153-166
We consider a generalization of the Minimum Spanning Tree Problem, called the Generalized Minimum Spanning Tree Problem, denoted by GMST. It is known that the GMST problem is NP-hard. We present a stronger result regarding its complexity, namely, the GMST problem is NP-hard even on trees as well an exact exponential time algorithm for the problem based on dynamic programming. We describe new mixed integer programming models of the GMST problem, mainly containing a polynomial number of constraints. We establish relationships between the polytopes corresponding to their linear relaxations. Based on a new model of the GMST we present a solution procedure that solves the problem to optimality for graphs with nodes up to 240. We discuss the advantages of our method in comparison with earlier methods. 相似文献
7.
B. A. Khudaigulyev 《Differential Equations》2012,48(2):255-263
We study the behavior of nonnegative solutions of the Dirichlet problem for a linear elliptic equation with a singular potential
in the ball B = B(0,R) ⊂ R
n
(n ≥ 3), R ≤ 1. We find an exact condition on the potential ensuring the existence or absence of a nonnegative solution of that problem. 相似文献
8.
André R. S. Amaral 《Optimization Letters》2009,3(4):513-520
We are concerned with the exact solution of a graph optimization problem known as minimum linear arrangement (MinLA). Define the length of each edge of a graph with respect to a linear ordering of the graph vertices. Then, the MinLA problem asks for a vertex
ordering that minimizes the sum of edge lengths. MinLA has several practical applications and is NP-Hard. We present a mixed
0-1 linear programming formulation of the problem, which led to fast optimal solutions for dense graphs of sizes up to n = 23. 相似文献
9.
Approximate Solutions of Continuous Dispersion Problems 总被引:1,自引:0,他引:1
The problem of positioning p points so as to maximize the minimum distance between them has been studied in both location theory (as the continuous p-dispersion problem) and the design of computer experiments (as the maximin distance design problem). This problem can be
formulated as a nonlinear program, either exactly or approximately. We consider formulations of both types and demonstrate
that, as p increases, it becomes dramatically more expensive to compute solutions of the exact formulation than to compute solutions
of the approximate formulation. 相似文献
10.
Dan Pritikin 《Journal of Graph Theory》1986,10(2):197-201
Graham and Pollak [2] proved that n – 1 is the minimum number of edge-disjoint complete bipartite subgraphs into which the edges of Kn decompose. Tverberg [6], using a linear algebraic technique, was the first to give a simple proof of this result. We apply Tverberg's technique to obtain results for two related decomposition problems, in which we wish to partition the arcs/edges of complete digraphs/multigraphs into a minimum number of arc/edge-disjoint complete bipartite subgraphs of appropriate natures. We obtain exact results for the digraph problem, which was posed by Lundgren and Maybee [4]. We also obtain exact results for the decomposition of complete multigraphs with exactly two edges connecting every pair of distinct vertices. 相似文献
11.
Solving the Vehicle Routing Problem with Stochastic Demands using the Cross-Entropy Method 总被引:8,自引:0,他引:8
An alternate formulation of the classical vehicle routing problem with stochastic demands (VRPSD) is considered. We propose a new heuristic method to solve the problem, based on the Cross-Entropy method. In order to better estimate the objective function at each point in the domain, we incorporate Monte Carlo sampling.
This creates many practical issues, especially the decision as to when to draw new samples and how many samples to use. We also develop a framework for obtaining exact solutions and tight lower bounds for the problem under various
conditions, which include specific families of demand distributions. This is used to assess the performance of the algorithm.
Finally, numerical results are presented for various problem instances to illustrate the ideas. 相似文献
12.
E. A. Zernyshkina 《Proceedings of the Steklov Institute of Mathematics》2009,265(1):199-207
We prove that there is no single uniform tight frame in Euclidean (unitary) space such that a solution of the ℓ
1-norm minimization problem for the frame representation is attained on the frame coefficients. Then we find an exact solution
of the ℓ
1-minimization problem for the Mercedes-Benz frame in ℝ
N
. We also give some examples of connections between optimization problems of various types. 相似文献
13.
We study the unique solvability of the Dirichlet problem for the biharmonic equation in the exterior of a compact set under the assumption that a generalized solution of this problem has a bounded Dirichlet integral with weight |x|a. Depending on the value of the parameter a,a we prove uniqueness theorems or present exact formulas for the dimension of the solution space of the Dirichlet problem. 相似文献
14.
We study the problem of designing fault tolerant routings in both complete and complete bipartite optical networks. We show that this problem has strong connections to various fundamental problems in design theory. Using a design theory approach, we find optimal f‐fault tolerant arc‐forwarding indexes for all complete networks and all complete balanced bipartite networks. Similarly, we find almost exact values for f‐fault tolerant optical indexes for these networks. © 2005 Wiley Periodicals, Inc. J Combin Designs 相似文献
15.
We consider the optimal recovery problem for the solution of the Dirichlet problem for the Laplace equation in the unit d-dimensional ball on a sphere of radius ρ from a finite collection of inaccurately specified Fourier coefficients of the solution on a sphere of radius r, 0 < r < ρ < 1. The methods are required to be exact on certain subspaces of spherical harmonics.
相似文献16.
S. Repin 《Journal of Mathematical Sciences》2009,159(2):229-240
We derive computable upper bounds of the difference between an exact solution of the initial boundary value problem for a
linear hyperbolic equation and any function in a space-time cylinder that belongs to the respective energy class. We prove
that the bounds vanish if and only if the approximate solution coincides with the exact one. Bibliography: 13 titles.
Dedicated to the jubilee of dear Nina Nikolaevna Uraltseva
Translated from Problemy Matematicheskogo Analiza, 41, May 2009, pp. 93–106. 相似文献
17.
Tadeusz Antczak Marcin Studniarski 《Numerical Functional Analysis & Optimization》2016,37(12):1465-1487
In this article, the vector exact l1 penalty function method used for solving nonconvex nondifferentiable multiobjective programming problems is analyzed. In this method, the vector penalized optimization problem with the vector exact l1 penalty function is defined. Conditions are given guaranteeing the equivalence of the sets of (weak) Pareto optimal solutions of the considered nondifferentiable multiobjective programming problem and of the associated vector penalized optimization problem with the vector exact l1 penalty function. This equivalence is established for nondifferentiable invex vector optimization problems. Some examples of vector optimization problems are presented to illustrate the results established in the article. 相似文献
18.
A rule for 3-way division of profits based on peer evaluation reports is impartial if the calculation of each partner’s share ignores her report, exact if it never allocates more or less than the profit to be shared, and consensual if it respects evaluations when the partners’ reports are in agreement. We use a calculus of variations technique to solve exactly a simple version of the problem of finding a 3-way exact, impartial division function of minimal average deviation from consensuality. We also give approximate solutions to three versions of the problem using a numerical analysis technique that is widely applicable. 相似文献
19.
We consider the maximization of a multicommodity flow throughput in presence of constraints on the maximum number of paths
to be used. Such an optimization problem is strongly NP-hard, and is known in the literature as the maximum routable demand fraction variant of the k-splittable flow problem. Here we propose an exact approach based on branch and bound rules and on an arc-flow mixed integer
programming formulation of the problem. Computational results are provided, and a comparison with a standard commercial solver
is proposed. 相似文献
20.
A. D. Lizarev 《Journal of Mathematical Sciences》1993,65(5):1848-1851
We find an exact solution of the problem of displacements and stresses in a polar-orthotropic annular plate of variable thickness with physico-mechanical properties of the material depending on temperature. The solutions are obtained as generalized and degenerate hypergeometric functions.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 33, 1991, pp. 42–45. 相似文献