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991.
Abstract. The global convergence of the general three-term conjugate gradient methods withthe relaxed strong Wolfe line-search is proved. 相似文献
992.
Ningning Yan 《Advances in Computational Mathematics》2001,15(1-4):333-361
In this paper, we present a posteriori error estimates of gradient recovery type for elliptic obstacle problems. The a posteriori error estimates provide both lower and upper error bounds. It is shown to be equivalent to the discretization error in an energy type norm for general meshes. Furthermore, when the solution is smooth and the mesh is uniform, it is shown to be asymptotically exact. Some numerical results which demonstrate the theoretical results are also reported in this paper. 相似文献
993.
In this paper, we derive gradient recovery type a posteriori error estimate for the finite element approximation of elliptic equations. We show that a posteriori error estimate provide both upper and lower bounds for the discretization error on the non-uniform meshes. Moreover, it is proved that a posteriori error estimate is also asymptotically exact on the uniform meshes if the solution is smooth enough. The numerical results demonstrating the theoretical results are also presented in this paper. 相似文献
994.
1 IntroductionThe K-S equation represents a class of pattern formation equations.It has beenstudied extensively in recent years,both in the context of inertial manifolds and finite-di-mensional attractors as well as in numerical simulations of system dynamical behaviour( see[2 ,4 ,7-1 0 ] ) .Despite many studies of dynamical behaviour of the K_ Sequation,the steady-state analysis of the equation has not been thoroughly carried out,which ispractically important and theoretically interesting.… 相似文献
995.
Charles S. Kahane 《Czechoslovak Mathematical Journal》2001,51(1):39-44
The author obtains an estimate for the spatial gradient of solutions of the heat equation, subject to a homogeneous Neumann boundary condition, in terms of the gradient of the initial data. The proof is accomplished via the maximum principle; the main assumption is that the sufficiently smooth boundary be convex. 相似文献
996.
1 IntroductionIn this paPer, we are interested in tlie time-asymptotic behavior of solutions to isentropicNavier-stokes equations in even space-dimensions. Recently many people began to study it'sasymptotic behavier when time is large enough. This can be manifested in tlie after refer-ences. For the pointwise estimate of solution to generaJ hyperbolic-parabolic systems in onespace dimension see Liu and Zeng[']. In several space variables, Kawashima[31 has studiedgeneral hyperbolic-parabolic… 相似文献
997.
Global Convergence of Conjugate Gradient Methods without Line Search 总被引:11,自引:0,他引:11
Global convergence results are derived for well-known conjugate gradient methods in which the line search step is replaced by a step whose length is determined by a formula. The results include the following cases: (1) The Fletcher–Reeves method, the Hestenes–Stiefel method, and the Dai–Yuan method applied to a strongly convex LC
1 objective function; (2) The Polak–Ribière method and the Conjugate Descent method applied to a general, not necessarily convex, LC
1 objective function. 相似文献
998.
Qing Chen 《Annals of Global Analysis and Geometry》2001,19(2):177-184
We obtain curvature estimates for certain stable minimalhypersurfaces in R
4 and R
5without using volume bounds. It follows that if M is acomplete stable minimal hypersurface in R
4 orR
5, then M is a hyperplane whenM intersects each extrinsic ball in, at most,N-components. 相似文献
999.
A three-parameter family of nonlinear conjugate gradient methods 总被引:3,自引:0,他引:3
In this paper, we propose a three-parameter family of conjugate gradient methods for unconstrained optimization. The three-parameter family of methods not only includes the already existing six practical nonlinear conjugate gradient methods, but subsumes some other families of nonlinear conjugate gradient methods as its subfamilies. With Powell's restart criterion, the three-parameter family of methods with the strong Wolfe line search is shown to ensure the descent property of each search direction. Some general convergence results are also established for the three-parameter family of methods. This paper can also be regarded as a brief review on nonlinear conjugate gradient methods.
1000.