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71.
Jianghua Fan 《Journal of Mathematical Analysis and Applications》2008,337(2):1041-1047
In this paper, we study the existence of solutions and approximation of the solutions by using a Mann type iterative scheme for variational inequalities in noncompact subsets of Banach spaces. The results presented in this paper generalize the corresponding results of J. Li [J. Li, On the existence of solutions of variational inequalities in Banach spaces, J. Math. Anal. Appl. 295 (2004) 115-126]. 相似文献
72.
模糊线性系统的扰动分析 总被引:1,自引:1,他引:0
使用谱范数分析了模糊线性系统在三种情形下的扰动: (1)右端模糊向量有扰动, 系数矩阵不变; (2)系数矩阵有扰动,右端模糊向量不变; (3)系数矩阵和右端模糊向量都有扰动,并通过数值实例验证给出的扰动界的估计. 相似文献
73.
J. Flachs 《Journal of Optimization Theory and Applications》1986,48(3):379-417
We present a unified technique for updating approximations to Jacobian or Hessian matrices when any linear structure can be imposed. The updates are derived by variational means, where an operator-weighted Frobenius norm is used, and are finally expressed as solutions of linear equations and/or unconstrained extrema. A certain behavior of the solutions is discussed for certain perturbations of the operator and the constraints. Multiple secant relations are then considered. For the nonsparse case, an explicit family of updates is obtained including Broyden, DFP, and BFGS. For the case where some of the matrix elements are prescribed, explicit solutions are obtained if certain conditions are satisfied. When symmetry is assumed, we show, in addition, the connection with the DFP and BFGS updates.This work was partially supported by a grant from Control Data 相似文献
74.
王奕人 《纯粹数学与应用数学》2010,26(4):701-704
在算术平均值和几何平均值的基础上,给出了一种新的平均值—拟算数平均值以及拟几何平均值,并将它们引入到Banach空间进行了讨论.给出了一些定义并在其基础上得到了这几类平均值在Banach空间中的几个有用的性质. 相似文献
75.
An iterative algorithm is proposed for finding a fixed point of a nonexpansive self-mapping of a closed convex subset of a Banach space with a uniformly Gâteaux differentiable norm, and an estimate of the convergence speed also is given. 相似文献
76.
Let E be a real reflexive Banach space having a weakly continuous duality mapping Jφ with a gauge function φ, and let K be a nonempty closed convex subset of E. Suppose that T is a non‐expansive mapping from K into itself such that F (T) ≠ ??. For an arbitrary initial value x0 ∈ K and fixed anchor u ∈ K, define iteratively a sequence {xn } as follows: xn +1 = αn u + βn xn + γn Txn , n ≥ 0, where {αn }, {βn }, {γn } ? (0, 1) satisfies αn +βn + γn = 1, (C 1) limn →∞ αn = 0, (C 2) ∑∞n =1 αn = ∞ and (B) 0 < lim infn →∞ βn ≤ lim supn →∞ βn < 1. We prove that {xn } converges strongly to Pu as n → ∞, where P is the unique sunny non‐expansive retraction of K onto F (T). We also prove that the same conclusions still hold in a uniformly convex Banach space with a uniformly Gâteaux differentiable norm or in a uniformly smooth Banach space. Our results extend and improve the corresponding ones by C. E. Chidume and C. O. Chidume [Iterative approximation of fixed points of non‐expansive mappings, J. Math. Anal. Appl. 318 , 288–295 (2006)], and develop and complement Theorem 1 of T. H. Kim and H. K. Xu [Strong convergence of modified Mann iterations, Nonlinear Anal. 61 , 51–60 (2005)]. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
77.
Karl Gustafson 《Linear algebra and its applications》2009,430(10):2762-2770
Three new applications of the author’s operator trigonometry are presented. These take place in three diverse mathematical domains: matrix statistics, numerical analysis, and theoretical physics. The goal is to continue to develop and expand the scope of the operator trigonometry. 相似文献
78.
T.别克 《数学物理学报(B辑英文版)》2005,25(4):681-686
1Introduction and PreliminariesThroughout this paper,we consider linear spaces over the complex numbers C.Given alinear space X and integers m and n,let Mm,n(X)=X?Mm,n denote the linear space ofm×n matricesx=?????x.x..m1,1,1.x..xm1,n,n?????with entries x… 相似文献
79.
P. Das N.R. Chakraborti P.K. Chaudhuri 《Computational Optimization and Applications》2001,18(3):311-326
This paper presents an algorithm for determining a minimax location to service demand points that are equally weighted and distributed over a sphere. The norm under consideration is geodesic. The algorithm presented here is based on enumeration and has a polynomial time complexity. 相似文献
80.
O. S. Dragoshanskii 《Mathematical Notes》2000,67(5):582-595
In the paper new estimates of anisotropic norms for trigonometric polynomials are obtained.
Translated fromMatematischeskie Zametki, Vol. 67, No. 5, pp. 686–701, May, 2000. 相似文献