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141.
Mathematical Notes - 相似文献
142.
The state of the art iterative method for solving large linear systems is the conjugate gradient (CG) algorithm. Theoretical convergence analysis suggests that CG converges more rapidly than steepest descent. This paper argues that steepest descent may be an attractive alternative to CG when solving linear systems arising from the discretization of ill-posed problems. Specifically, it is shown that, for ill-posed problems, steepest descent has a more stable convergence behavior than CG, which may be explained by the fact that the filter factors for steepest descent behave much less erratically than those for CG. Moreover, it is shown that, with proper preconditioning, the convergence rate of steepest descent is competitive with that of CG.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
143.
Somyot Plubtieng Rattanaporn Punpaeng 《Journal of Mathematical Analysis and Applications》2007,336(1):455-469
In this paper, we introduce two iterative schemes by the general iterative method for finding a common element of the set of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. Then, we prove two strong convergence theorems for nonexpansive mappings to solve a unique solution of the variational inequality which is the optimality condition for the minimization problem. These results extended and improved the corresponding results of Marino and Xu [G. Marino, H.K. Xu, A general iterative method for nonexpansive mapping in Hilbert spaces, J. Math. Anal. Appl. 318 (2006) 43-52], S. Takahashi and W. Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (1) (2007) 506-515], and many others. 相似文献
144.
Yu Zanping Zhou Zheyan School of Math.and Computer Science Fujian Normal University Fuzhou ) Shen Jianhe 《Annals of Differential Equations》2007,23(3):365-372
The paper aims to obtain existence and uniqueness of the solution as well as asymptotic estimate of the solution for singularly perturbed nonlinear third- order Robin boundary value problem with a turning point.In order to achieve this aim,existence and uniqueness of the solution for third-order nonlinear Robin boundary value problem is derived first based on the upper and lower solutions method under relatively weaker conditions.In this manner,the goal of this paper is gained by applying the existence and uniqueness results mentioned above. 相似文献
145.
A time-dependent model corresponding to an Oldroyd-B viscoelastic fluid is considered, the convective terms being disregarded.
Global existence in time is proved in Banach spaces provided the data are small enough, using the implicit function theorem
and a maximum regularity property for a three fields Stokes problem. A finite element discretization in space is then proposed.
Existence of the numerical solution is proved for small data, so as a priori error estimates, using again an implicit function
theorem.
Supported by the Swiss National Science Foundation. Fellowship PBEL2–114311. 相似文献
146.
Lower-dimensional linear complementarity problem approaches to the solution of a bi-obstacle problem
A globally convergent Broyden-like method for solving a bi-obstacle problem is proposed based on its equivalent lower-dimensional linear complementarity problem. A suitable line search technique is introduced here. The global and superlinear convergence of the method is verified under appropriate assumptions. 相似文献
147.
Chu-Li Fu Xiang-Tuan Xiong Zhi Qian 《Journal of Mathematical Analysis and Applications》2007,331(1):472-480
In this paper a simple and convenient new regularization method for solving backward heat equation—Fourier regularization method is given. Meanwhile, some quite sharp error estimates between the approximate solution and exact solution are provided. A numerical example also shows that the method works effectively. 相似文献
148.
Noureddine Igbida 《Journal of Mathematical Analysis and Applications》2007,335(2):1061-1078
In this paper, we study the nonlinear evolution equation of Hele-Shaw type with dynamical boundary conditions. That is, the equation ut=Δw+f where u∈H(w) and H is the Heaviside function, with boundary condition μ(x,w)t∂w+k∇w⋅ν=g, where ν denotes the outward normal vector of the fixed boundary of the domain. We prove existence, uniqueness and some qualitative properties of the solution. 相似文献
149.
Wuqing Ning 《Journal of Mathematical Analysis and Applications》2007,327(2):1396-1419
In this paper, an algorithm is established to reconstruct an eigenvalue problem from the given data satisfying certain conditions. These conditions are proved to be not only necessary but also sufficient for the given data to coincide with the spectral characteristics corresponding to the reconstructed eigenvalue problem. 相似文献
150.
Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional
random vectors with various types of symmetries. In particular, we obtain results for distributions which are coordinatewise
symmetric, uniform in a regular simplex, or spherically symmetric. Our proofs are based on Stein’s method of exchangeable
pairs; as far as we know, this approach has not previously been used in convex geometry. The spherically symmetric case is
treated by a variation of Stein’s method which is adapted for continuous symmetries.
This work was done while at Stanford University. 相似文献