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151.
An adaptive trust region method and its convergence 总被引:17,自引:0,他引:17
In this paper, a new trust region subproblem is proposed. The trust radius in the new subproblem adjusts itself adaptively.
As a result, an adaptive trust region method is constructed based on the new trust region subproblem. The local and global
convergence results of the adaptive trust region method are proved. Numerical results indicate that the new method is very
efficient. 相似文献
152.
Roman Dwilewicz Joë l Merker 《Proceedings of the American Mathematical Society》2002,130(7):1975-1980
Let be a compact, connected, -smooth and globally minimal hypersurface in which divides the projective space into two connected parts and . We prove that there exists a side, or , such that every continuous CR function on extends holomorphically to this side. Our proof of this theorem is a simplification of a result originally due to F. Sarkis.
153.
Yuxiang Li Weibing Deng Chunhong Xie 《Proceedings of the American Mathematical Society》2002,130(12):3661-3670
The initial-boundary value problems are considered for the strongly coupled degenerate parabolic system
in the cylinder , where is bounded and are positive constants. We are concerned with the global existence and nonexistence of the positive solutions. Denote by the first Dirichlet eigenvalue for the Laplacian on . We prove that there exists a global solution iff .
in the cylinder , where is bounded and are positive constants. We are concerned with the global existence and nonexistence of the positive solutions. Denote by the first Dirichlet eigenvalue for the Laplacian on . We prove that there exists a global solution iff .
154.
The authors consider the nonlinear difference equation xn+1=xn+xn-kf(xn-k),n=0,1,(0.1) where (0,1), k 0,1, and f C1[[0,), [0,)] with f(x) < 0.They give sufficient conditions for the unique positive equilibrium of (0.1) to be a global attractor of all positive solutions. The results here are somewhat easier to apply than those of other authors. An application to a model of blood cell production is given. 相似文献
155.
1.引言考虑非线性代数方程组这里, 为连续的对角映射,二者的导函数均存在,但并不一定连续.这类非线性代数方程组具有丰富的实际背景.譬如,Stefan问题和许多弱非线性椭圆型偏微分方程,就可归结为(1.1)的数值求解问题.根据方程组(1.1)的特殊结构,并利用矩阵多重分裂思想,文tZ]讨论了一类并行非线性Gauss-Seidel型迭代算法.这类算法具有很好的数值性质和较高的并行效率·在此基础上,运用松弛加速技术,文[8]进一步研究了一类并行多分… 相似文献
156.
1.引言随着无限维动力系统研究的发展和深入,人们对非线性发展方程长时间性态的研究越来越重视[1-6],而这种研究在很大程度上依赖于数值计算的结果,因此,计算结果是否可靠,计算格式先得是否合适都是值得探讨和深入研究的问题17-10.广义KdV-Burg6rs方程是一类重要的非线性发展方程,在实际问题中也有着广泛的应用,因此,对它的研究即有理论价值也有实际意义.本文讨论如下的广义KdV-Burgers方程的周期初值问题其中a,q是已知实常数,且a>0八。),g(。),h00是已知实函数.文[10]对上述问题构造了半离散的Fourier谱逼近… 相似文献
157.
J. Bourgain 《Journal of the American Mathematical Society》1999,12(1):145-171
We establish global wellposedness and scattering for the -critical defocusing NLS in 3D
assuming radial data , . In particular, it proves global existence of classical solutions in the radial case. The same result is obtained in 4D for the equation
158.
In this paper, we consider a predator-prey system with stage structure and harvesting (where the predator population has two stages, an immature stage and a mature stage with harvesting, and the growth of the prey population is of Lotka-Volterra nature). We obtain the conditions of the globally asymptotic stability for three nonne-gative equilibria of this system. 相似文献
159.
S. K. Zavriev 《Journal of Optimization Theory and Applications》1996,91(1):185-214
The steepest-descent technique dealing with the perturbed values of the objective function and its gradients and with nonexact line searches is considered. Attention is given to the case where the perturbations do not decrease on the algorithm trajectories; the aim is to investigate how perturbations at every iteration of the algorithm perturb its original attractor set.Based on the Liapunov direct method for attraction analysis of discrete-time processes, a sharp estimation of the attractor set generated by a perturbed steepest-descent technique with respect to the perturbation magnitudes is obtained. Some global optimization properties of finite-difference analogues of the gradient method are discovered. These properties are not inherent in methods which use exact gradients.The author is grateful to the referees for many useful suggestions. 相似文献
160.
赵会江 《数学物理学报(B辑英文版)》1996,(3)
FIRSTORDERQUASILINEAREQUATIONSINSEVERALINDEPENDENTVARIABLESWITHSINGULARINITIALDATAL~p(P<∞)¥(赵会江)ZhaoHuijiang(YoungScientistLa?.. 相似文献