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71.
Convergence analysis of implicit iterative algorithms for asymptotically nonexpansive mappings 总被引:1,自引:0,他引:1
In this paper, we consider the weak and strong convergence of an implicit iterative process with errors for two finite families of asymptotically nonexpansive mappings in the framework of Banach spaces. Our results presented in this paper improve and extend the recent ones announced by many others. 相似文献
72.
Banach空间中渐近非扩张映象具误差的强收敛定理 总被引:2,自引:0,他引:2
设E是一实的Banach空间,其范数是一致Gteaux可微的;D是E的一非空闭凸子集,设T:D→D是具有序列{k_n}[1,∞),lim_(n→∞) k_n=1的渐近非扩张映象.本文证明了,在一定条件下,由(1.3)和(1.5)式定义的具误差的迭代序列{x_n}强收敛于T的不动点.本文结果也推广和改进了最近一些人的最新结果. 相似文献
73.
T. Binder L. Blank W. Dahmen W. Marquardt 《Journal of Optimization Theory and Applications》2001,111(3):529-551
Usually, direct methods are employed for the solution of linear systems arising in the context of optimization. However, motivated by the potential of multiscale refinement schemes for large problems of dynamic state estimation, we investigate in this paper the application of iterative solvers based on the concepts developed in Ref. 1. Specifically, we explore the effect of different system reductions for various Krylov-space iteration methods as well as three concepts of preconditioning. The first one is the normalization of states and outputs, which also favors error analysis. Next, diagonal scale-dependent preconditioners are compared; they all bound the condition numbers independently of the refinement scale, but exhibit significant quantitative differences. Finally, the effect of the regularization parameter on condition numbers and iteration numbers is analyzed. It turns out that a so-called simplified Uzawa scheme with Jacobi preconditioning and suitable regularization parameter is most efficient. The experiments also reveal that further improvements are necessary. 相似文献
74.
In this paper,we are interested in HSS preconditioners for saddle point lin- ear systems with a nonzero(2,2)-th block.We study an approximation of the spectra of HSS preconditioned matrices and use these results to illustrate and explain the spectra obtained from numerical examples,where the previous spectral analysis of HSS precon- ditioned matrices does not cover. 相似文献
75.
本文利用原始变量有限元法求解混合边界条件下的三维定常旋转Navier-Stokes方程,证明了离散问题解的存在唯一性,得到了有限元解的最优误差估计.给出了求解原始变量有限元逼近解的简单迭代算法,并证明了算法的收敛性.针对三维情况下计算资源的限制,采用压缩的行存储格式存储刚度矩阵的非零元素,并利用不完全的LU分解作预处理的GMRES方法求解线性方程组.最后分析了简单迭代和牛顿迭代的优劣对比,数值算例表明在同样精度下简单迭代更节约计算时间. 相似文献
76.
A. Alsaad A. Ahmad 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,54(2):151-156
First-principles calculations are performed to compute the e33
piezoelectric coefficients of GaN, ScN and (ScxGa1-xN) alloys
exhibiting an alternation of hexagonal GaN, with hexagonal ScN along the c-axis. For Sc compositions larger than 50%, each atom has nearly five nearest
neighbors (i.e., the ground state exhibits a phase that is five-fold
coordinated). On the other hand, Sc-deficient (Sc, Ga) N alloys adopt a
ground-state that is four-fold coordinated). The magnitude of e33 in
the Sc-deficient ideally ordered (Sc0.25Ga0.75N) is found to be larger
than the magnitude of the corresponding e33 coefficients resulting from
the compositional weighted average over the hexagonal (h-ScN) and the wurtzite (w-GaN) parent compounds. On the other hand, the e33 coefficients of the Sc-rich
ordered (Sc0.75Ga0.25N) is found to be negligibly small. In addition, e33
piezoelectric coefficients in ordered (Sc0.5Ga0.5N) exhibit quite
large magnitudes, due to the nonpolar to polar transition occurs at Sc composition x = 0.5, and thus can bridge the corresponding coefficients of (Ga, In) N and
ferroelectric alloys. The microscopic origins for this huge enhancement in
the piezoelectric behavior in Sc-low and Sc-intermediate alloys and the role
of each atom are revealed and discussed. 相似文献
77.
Meta-learning, or “learning to learn”, refers to techniques that infer an inductive bias from data corresponding to multiple related tasks with the goal of improving the sample efficiency for new, previously unobserved, tasks. A key performance measure for meta-learning is the meta-generalization gap, that is, the difference between the average loss measured on the meta-training data and on a new, randomly selected task. This paper presents novel information-theoretic upper bounds on the meta-generalization gap. Two broad classes of meta-learning algorithms are considered that use either separate within-task training and test sets, like model agnostic meta-learning (MAML), or joint within-task training and test sets, like reptile. Extending the existing work for conventional learning, an upper bound on the meta-generalization gap is derived for the former class that depends on the mutual information (MI) between the output of the meta-learning algorithm and its input meta-training data. For the latter, the derived bound includes an additional MI between the output of the per-task learning procedure and corresponding data set to capture within-task uncertainty. Tighter bounds are then developed for the two classes via novel individual task MI (ITMI) bounds. Applications of the derived bounds are finally discussed, including a broad class of noisy iterative algorithms for meta-learning. 相似文献
78.
利用Mann迭代技巧,讨论了一类随机算子方程A(ω,x(ω),x(ω))=B(ω,x(ω))的随机解的存在唯一性,并给出了迭代序列收敛于解的误差估计,所得结果是某些已知结果本质改进和推广. 相似文献
79.
Vladimir Schmidt Roman Schuh 《Journal of Quantitative Spectroscopy & Radiative Transfer》2011,112(11):1705-1710
Different preconditioning techniques for the iterative method MinRes as solver for the Discrete Sources Method (DSM) are presented. This semi-analytical method is used for light scattering computations by particles in the Mie scattering regime. Its numerical schema includes a linear least-squares problem commonly solved using the QR decomposition method. This could be the subject of numerical difficulties and instabilities for very large particles or particles with extreme geometry. In these cases, we showed that iterative methods with preconditioning techniques can provide a satisfying solution.In our previous paper, we studied four different iterative solvers (RGMRES, BiCGStab, BiCGStab(l), and MinRes) considering the performance and the accuracy of a solution. Here, we study several preconditioning techniques for the MinRes method for a variety of oblate and prolate spheroidal particles of different size and geometrical aspect ratio. Using preconditioning techniques we highly accelerated the iterative process especially for particles with a higher aspect ratio. 相似文献
80.
Roman Schuh Thomas Wriedt 《Journal of Quantitative Spectroscopy & Radiative Transfer》2011,112(11):1697-1704
The implementation of iterative methods as solvers for the Discrete Sources Method (DSM) is presented. In this method, light scattering computation linear systems with dense and relative small matrices are generated. The linear systems are traditionally solved using the QR-decomposition method. For large particles or particles with extreme geometries even this commonly stable solver can fail. In these cases, we expect that iterative methods can provide a satisfying solution nevertheless.We will present our investigation in two consecutive papers. Here, we study four different iterative solvers (RGMRES, BiCGStab, BiCGStab(l), and MinRes) considering the performance and the accuracy for typical light scattering problems. Using these iterative methods we increased the quality of a solution, especially for oblate spheroids with a higher aspect ratio. Preconditioning technique is considered in the following paper. 相似文献