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31.
A new test for strict monotonicity of the regression function is proposed which is based on a composition of an estimate of
the inverse of the regression function with a common regression estimate. This composition is equal to the identity if and
only if the “true” regression function is strictly monotone, and a test based on an L
2-distance is investigated. The asymptotic normality of the corresponding test statistic is established under the null hypothesis
of strict monotonicity.
相似文献
32.
R-linear convergence of the Barzilai and Borwein gradient method 总被引:4,自引:0,他引:4
Combined with non-monotone line search, the Barzilai and Borwein(BB) gradient method has been successfully extended for solvingunconstrained optimization problems and is competitive withconjugate gradient methods. In this paper, we establish theR-linear convergence of the BB method for any-dimensional stronglyconvex quadratics. One corollary of this result is that theBB method is also locally R-linear convergent for general objectivefunctions, and hence the stepsize in the BB method will alwaysbe accepted by the non-monotone line search when the iterateis close to the solution. 相似文献
33.
EXISTENCE OF SOLUTIONS OF A FAMILY OF NONLINEAR BOUNDARY VALUE PROBLEMS IN L~2-SPACES 总被引:1,自引:0,他引:1
Wei Li Zhou HaiyunSchool of Mathematics Statistics Hebei University of Economics Business Shijiazhuang China. Inst.of Appl.Math.and Mech. Ordnance Engineering College Shijiazhuang China. 《高校应用数学学报(英文版)》2005,(2)
§ 1 Introduction and preliminariesThe equations related to the p- L aplacian operatorΔp have been studied in differentaspects[1— 4 ] sinceΔp arises from a variety of physical phenomena such as non Newtonianfluids,reaction- diffusion problems,etc.In this paper,the following equation(1) which canbe regarded as an extension of those in[1— 4 ]will be discussed:- div(α(gradu) ) +|u(x) |p- 2 u(x) +g(x,u(x) ) =f (x) a.e. onΩ-〈n,α(gradu)〉∈βx(u(x) ) ,a.e.onΓ . (1) More details can b… 相似文献
34.
The 1-Lipschitz mapping between the unit spheres of two Hilbert spaces can be extended to a real linear isometry of the whole space 总被引:18,自引:0,他引:18
定光桂 《中国科学A辑(英文版)》2002,45(4):479-483
LetE andF be Hilbert spaces with unit spheresS
1(E) andS
1(F). Suppose thatV
0 S1(E) →S
1(F) is a Lipschitz mapping with Lipschitz constantk=1 such that −V
0[S
1(E)] ⊂V
0[S
1(E)]. Then V0 can be extended to a real linear isometric mappingV fromE intoF. In particular, every isometric mapping fromS
1(E) ontoS
1(F) can be extended to a real linear isometric mapping fromE ontoF. 相似文献
35.
36.
研究了非奇H-矩阵的判定问题.先给出了几个判定严格α-双链对角占优矩阵的充要条件,进一步利用矩阵对角占优理论得到了判定非奇H-矩阵的一些充分条件,推广和改进了已有的相关结果,并用数值算例说明了这些判定方法的有效性. 相似文献
37.
利用严格对角占优M-矩阵的逆矩阵的无穷大范数的范围,给出了B-矩阵线性互补问题误差界新的估计式.相应数值算例表明了结果的有效性. 相似文献
38.
是以机器人及其安全系统所构成的一个可修复系统作为研究对象,运用泛函分析方法并结合C_0半群理论,证明了严格占优本征值在本系统的存在性并且是系统严格占优本征值,进一步证明了在一定条件下,系统的动态解以指数化形式收敛于系统的稳态解. 相似文献
39.
Strong convergence theorems for strictly asymptotically pseudocontractive mappings in Hilbert spaces
Shi Sheng Zhang 《数学学报(英文版)》2011,27(7):1367-1378
The purpose of this paper is by using CSQ method to study the strong convergence problem of iterative sequences for a pair of strictly asymptotically pseudocontractive mappings to approximate a common fixed point in a Hilbert space. Under suitable conditions some strong convergence theorems are proved. The results presented in the paper are new which extend and improve some recent results of Acedo and Xu [Iterative methods for strict pseudo-contractions in Hilbert spaces. Nonlinear Anal., 67(7), 2258??271 (2007)], Kim and Xu [Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups. Nonlinear Anal., 64, 1140??152 (2006)], Martinez-Yanes and Xu [Strong convergence of the CQ method for fixed point iteration processes. Nonlinear Anal., 64, 2400??411 (2006)], Nakajo and Takahashi [Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups. J. Math. Anal. Appl., 279, 372??79 (2003)], Marino and Xu [Weak and strong convergence theorems for strict pseudocontractions in Hilbert spaces. J. Math. Anal. Appl., 329(1), 336??46 (2007)], Osilike et al. [Demiclosedness principle and convergence theorems for k-strictly asymptotically pseudocontractive maps. J. Math. Anal. Appl., 326, 1334??345 (2007)], Liu [Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings. Nonlinear Anal., 26(11), 1835??842 (1996)], Osilike et al. [Fixed points of demi-contractive mappings in arbitrary Banach spaces. Panamer Math. J., 12 (2), 77??8 (2002)], Gu [The new composite implicit iteration process with errors for common fixed points of a finite family of strictly pseudocontractive mappings. J. Math. Anal. Appl., 329, 766??76 (2007)]. 相似文献
40.
In this paper, based on the smooth point of the unit ball and its support linear functional,we show two equivalent formulations of the isometric extension problem between the unit spheres of strictly convex two-dimensional normed spaces. We prove that these equivalent formulations have a positive answer in a special case. 相似文献