首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we investigate the problem for finding the set of solutions for equilibrium problems, the set of solutions of the variational inequalities for k-Lipschitz continuous mappings and fixed point problems for nonexpansive mappings in a Hilbert space. We introduce a new viscosity extragradient approximation method which is based on the so-called viscosity approximation method and extragradient method. We show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions. Finally, we utilize our results to study some convergence problems for finding the zeros of maximal monotone operators. Our results are generalization and extension of the results of Kumam [P. Kumam, Strong convergence theorems by an extragradient method for solving variational inequalities and equilibrium problems in a Hilbert space, Turk. J. Math. 33 (2009) 85–98], Wangkeeree [R. Wangkeeree, An extragradient approximation method for equilibrium problems and fixed point problems of a countable family of nonexpansive mappings, Fixed Point Theory and Applications, 2008, Article ID 134148, 17 pages, doi:10.1155/2008/134148], Yao et al. [Y. Yao, Y.C. Liou, R. Chen, A general iterative method for an finite family of nonexpansive mappings, Nonlinear Analysis 69 (5–6) (2008) 1644–1654], Qin et al. [X. Qin, M. Shang, Y. Su, A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces, Nonlinear Analysis (69) (2008) 3897–3909], and many others.  相似文献   

2.
In this paper, we apply the Adomian decomposition method and Padé-approximate to solving the differential-difference equations (DDEs) for the first time. A simple but typical example is used to illustrate the validity and the great potential of the Adomian decomposition method (ADM) in solving DDEs. Comparisons are made between the results of the proposed method and exact solutions. The results show that ADM is an attractive method in solving the differential-difference equations.  相似文献   

3.
A method for estimating the distribution of scan statistics with high precisìon was introduced in Haiman (2000). Using that method sharp bounds for the errors were also established. This paper is concerned with the application of the method in Haiman (2000) to a two-dimensional Poisson process. The method involves the estimation by simulation of the conditional (fixed number of points) distribution of scan statistics for the particular rectangle sets of size 2 × 2, 2 × 3, 3 × 3, where the unit is the (1 × 1) dimension of the squared scanning window. In order to perform these particular estimations, we develop and test a perfect simulation algorithm. We then perform several numerical applications and compare our results with results obtained by other authors.  相似文献   

4.
An implicit-explicit (IMEX) method is developed for the numerical solution of reaction-diffusion equations with pure Neumann boundary conditions. The corresponding method of lines scheme with finite differences is analyzed: explicit conditions are given for its convergence in the ‖·‖ norm. The results are applied to a model for determining the overpotential in a proton exchange membrane (PEM) fuel cell.  相似文献   

5.
We present an alternative method for the numerical simulation of elasto-plastic material behaviour. For this extended Finite Element (FE) formulation the history variables, which provide the information of plastic deformations from the previous timesteps, are represented as FE functions. This results in additional degrees of freedom (DOF), and the radial return of the standard formulation is replaced by a fully coupled Newton method for the extended system. Numerical studies, using viscoplastic regularization within a geometrically linear approach prove comparative results and an advantage in calculation time for the extended FE formulation. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

6.
Frank Pörner 《PAMM》2016,16(1):787-788
In the present work, we present numerical results for an iterative method for solving an optimal control problem with inequality contraints. The method is based on generalized Bregman distances. Under a combination of a source condition and a regularity condition on the active sets convergence results are presented. Furthermore we show by numerical examples that the provided a-priori estimate is sharp in the bang-bang case. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

7.
In this paper, we develop an efficient preconditioning method on the basis of the modified hierarchy basis for solving the singular boundary value problem by the Galerkin method. After applying the preconditioning method, we show that the condition number of the linear system arising from the Galerkin method is uniformly bounded. In particular, the condition number of the preconditioned system will be bounded by 2 for the case q(x)=0 (see Eq. (1) in the paper). Numerical results are presented to confirm our theoretical results.  相似文献   

8.
In this paper, we give sufficient conditions for the convergence of the (AOR) method, when the matrix A for Ax = b is a strictly diagonally dominant matrix. These results improve the conclusions obtained in the Theorem 4 [10].With the notion of generalized diagonal dominant matrix, we enlarge the convergence regions given in Theorem 9 [10], when A is a nonsingular H-matrix.In the last section we generalize theorem 6 of Robert [11] and we present some results which extend the convergence regions for the (AOR) method.  相似文献   

9.
A modified conjugate gradient method is presented for solving unconstrained optimization problems, which possesses the following properties: (i) The sufficient descent property is satisfied without any line search; (ii) The search direction will be in a trust region automatically; (iii) The Zoutendijk condition holds for the Wolfe–Powell line search technique; (iv) This method inherits an important property of the well-known Polak–Ribière–Polyak (PRP) method: the tendency to turn towards the steepest descent direction if a small step is generated away from the solution, preventing a sequence of tiny steps from happening. The global convergence and the linearly convergent rate of the given method are established. Numerical results show that this method is interesting.  相似文献   

10.
In this paper we discuss split-step forward methods for solving Itô stochastic differential equations (SDEs). Eight fully explicit methods, the drifting split-step Euler (DRSSE) method, the diffused split-step Euler (DISSE) method and the three-stage Milstein (TSM 1a-TSM 1f) methods, are constructed based on Euler-Maruyama method and Milstein method, respectively, in this paper. Their order of strong convergence is proved. The analysis of stability shows that the mean-square stability properties of the methods derived in this paper are improved on the original methods. The numerical results show the effectiveness of these methods in the pathwise approximation of Itô SDEs.  相似文献   

11.
A finite difference scheme for estimating parameters in linear differential-delay equations is investigated. Convergence results and rates of convergence are obtained for a simple explicit (Euler's) method. Numerical examples are given to illustrate the convergence for the Euler method. Numerical results for a “higher order” scheme are also discussed.  相似文献   

12.
In this paper, we first provide comparison results of several types of the preconditioned AOR (PAOR) methods for solving a linear system whose coefficient matrix is an L-matrix satisfying some weaker conditions than those used in the recent literature. Next, we propose an application of PAOR method to a preconditioner of Krylov subspace method. Lastly, numerical results are provided to show that Krylov subspace method with the PAOR preconditioner performs quite well as compared with the ILU (0) preconditioner.  相似文献   

13.
The resonator problem for a positive branch confocal unstable resonator reduces to a Fredholm homogeneous integral equation of the second kind, whose numerical solution here is based on a sequence of algebraic eigenvalue problems. We compare two algorithms for the solution of an optical resonator problem. These are obtained by (i) successive degenerate kernel approximation by Taylor polynomials of the Fredholm kernel and (ii) Nyström’s method with Simpson’s rule as the subordinate numerical integration method. The numerical results arising from these routines compare well with other published results, and have the added advantage of simplicity and easy adaptability to other resonator problems.  相似文献   

14.
In this paper we prove rigorous results on persistence of invariant tori and their whiskers. The proofs are based on the parameterization method of [X. Cabré, E. Fontich, R. de la Llave, The parameterization method for invariant manifolds. I. Manifolds associated to non-resonant subspaces, Indiana Univ. Math. J. 52 (2) (2003) 283-328; X. Cabré, E. Fontich, R. de la Llave, The parameterization method for invariant manifolds. II. Regularity with respect to parameters, Indiana Univ. Math. J. 52 (2) (2003) 329-360]. The invariant manifolds results proved here include as particular cases of the usual (strong) stable and (strong) unstable manifolds, but also include other non-resonant manifolds. The method lends itself to numerical implementations whose analysis and implementation is studied in [A. Haro, R. de la Llave, A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: Numerical algorithms, preprint, 2005; A. Haro, R. de la Llave, A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: Numerical implementation and examples, preprint, 2005]. The results are stated as a posteriori results. Namely, that if one has an approximate solution which is not degenerate, then, one has a true solution not too far from the approximate one. This can be used to validate the results of numerical computations.  相似文献   

15.
We present an elementary method for proving enumeration formulas which are polynomials in certain parameters if others are fixed and factorize into distinct linear factors over Z. Roughly speaking the idea is to prove such formulas by “explaining” their zeros using an appropriate combinatorial extension of the objects under consideration to negative integer parameters. We apply this method to prove a new refinement of the Bender-Knuth (ex-)Conjecture, which easily implies the Bender-Knuth (ex-)Conjecture itself. This is probably the most elementary way to prove this result currently known. Furthermore we adapt our method to q-polynomials, which allows us to derive generating function results as well. Finally we use this method to give another proof for the enumeration of semistandard tableaux of a fixed shape which differs from our proof of the Bender-Knuth (ex-)Conjecture in that it is a multivariate application of our method.  相似文献   

16.
In this paper boundary procedures are discussed for a new secondorder accurate method, developed in Morris (1972) and Zwas,Eilon & Gottlieb (1972), for non-linear hyperbolic systemsin two space variables. This method is a multilevel scheme ofthe same type as those of Strang, (1964, 1968). It is shownthat the straightforward method of incorporating boundary datagives, in general, only locally first order accurate values.A boundary procedure which preserves local second order accuracyis developed. The method is also extended to systems in manyspace variables. The results of some numerical experiments arereported.  相似文献   

17.
A general approach to transference principles for discrete and continuous operator (semi)groups is described. This allows one to recover the classical transference results of Calderón, Coifman and Weiss and of Berkson, Gillespie and Muhly and the more recent one of the author. The method is applied to derive a new transference principle for (discrete and continuous) operator semigroups that need not be groups. As an application, functional calculus estimates for bounded operators with at most polynomially growing powers are derived, leading to a new proof of classical results by Peller from 1982. The method allows for a generalization of his results away from Hilbert spaces to Lp-spaces and—involving the concept of γ-boundedness—to general Banach spaces. Analogous results for strongly-continuous one-parameter (semi)groups are presented as well. Finally, an application is given to singular integrals for one-parameter semigroups.  相似文献   

18.
We introduce a novel modification to standard support vector machine (SVM) formulations based on a limited amount of penalty-free slack to reduce the influence of misclassified samples or outliers. We show that free slack relaxes support vectors and pushes them towards their respective classes, hence we use the name relaxed support vector machines (RSVM) for our method. We present theoretical properties of the RSVM formulation and develop its dual formulation for nonlinear classification via kernels. We show the connection between the dual RSVM and the dual of the standard SVM formulations. We provide error bounds for RSVM and show it to be stable, universally consistent and tighter than error bounds for standard SVM. We also introduce a linear programming version of RSVM, which we call RSVMLP. We apply RSVM and RSVMLP to synthetic data and benchmark binary classification problems, and compare our results with standard SVM classification results. We show that relaxed influential support vectors may lead to better classification results. We develop a two-phase method called RSVM2 for multiple instance classification (MIC) problems, where RSVM formulations are used as classifiers. We extend the two-phase method to the linear programming case and develop RSVMLP2. We demonstrate the classification characteristics of RSVM2 and RSVMLP2, and report our classification results compared to results obtained by other SVM-based MIC methods on public benchmark datasets. We show that both RSVM2 and RSVMLP2 are faster and produce more accurate classification results.  相似文献   

19.
Abstract

In this article, a projection-type method for mixed variational inequalities is proposed in Hilbert spaces. The proposed method has the following nice features: (i) The algorithm is well defined whether the solution set of the problem is nonempty or not, under some mild assumptions; (ii) If the solution set is nonempty, then the sequence generated by the method is strongly convergent to the solution, which is closest to the initial point; (iii) The existence of the solutions to variational inequalities can be verified through the behavior of the generated sequence. The results presented in this article generalize and improve some known results.  相似文献   

20.
We consider a numerical method based on the so-called “orthogonality condition” for the approximation and continuation of invariant tori under flows. The basic method was originally introduced by Moore [Computation and parameterization of invariant curves and tori, SIAM J. Numer. Anal. 15 (1991) 245–263], but that work contained no stability or consistency results. We show that the method is unconditionally stable and consistent in the special case of a periodic orbit. However, we also show that the method is unstable for two-dimensional tori in three-dimensional space when the discretization includes even numbers of points in both angular coordinates, and we point out potential difficulties when approximating invariant tori possessing additional invariant sub-manifolds (e.g., periodic orbits). We propose some remedies to these difficulties and give numerical results to highlight that the end method performs well for invariant tori of practical interest.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号