共查询到20条相似文献,搜索用时 31 毫秒
1.
Hong CHEN Luo-qing LI~ Faculty of Mathematics Computer Science Hubei University Wuhan China 《中国科学A辑(英文版)》2007,50(11):1529-1536
The multi-category classification algorithms play an important role in both theory and practice of machine learning.In this paper,we consider an approach to the multi-category classification based on minimizing a convex surrogate of the nonstandard misclassification loss.We bound the excess misclassification error by the excess convex risk.We construct an adaptive procedure to search the classifier and furthermore obtain its convergence rate to the Bayes rule. 相似文献
2.
We consider the classification problem by learning from samples drawn from a non-identical sequence of probability measures.
The learning algorithm is from Tikhonov regularization schemes associated with convex loss functions and reproducing kernel
Hilbert spaces. Our main goal is to provide satisfactory estimates for the excess misclassification error of the produced
classifiers. 相似文献
3.
We show that on some open sets, more general than balls, Runge approximation is possible in certain Banach spaces, and also in certain complex Banach manifolds. We also show that there is an entire holomorphic curve in Hilbert space on which there is a bounded holomorphic function on the trace of a ball that has no bounded holomorphic extension to even a smaller concentric ball. Using the same technique we also prove that a form of Runge approximation better than an error function is not always possible. 相似文献
4.
LIU Taishun & XU Qinghua Department of Mathematics Huzhou Teachers College Huzhou China Department of Mathematics Jiangxi Normal University Nanchang China 《中国科学A辑(英文版)》2006,(11)
In this paper, a class of biholomorphic mappings named quasi-convex mapping of order a in the unit ball of a complex Banach space is introduced. When the Banach space is confined to Cn, we obtain the relation between this class of mappings and the convex mappings. Furthermore, the growth and covering theorems of this class of mappings are given on the unit ball of a complex Banach space X. Finally, we get the second order terms coefficient estimations of the homogeneous expansion of quasi-convex mapping of order a defined on the polydisc in Cn and on the unit ball in a complex Banach space, respectively. 相似文献
5.
In this paper, a class of biholomorphic mappings named quasi-convex mapping of order α in the unit ball of a complex Banach space is introduced. When the Banach space is confined to Cn, we obtain the relation between this class of mappings and the convex mappings.Furthermore, the growth and covering theorems of this class of mappings are given on the unit ball of a complex Banach space Ⅹ. Finally, we get the second order terms coefficient estimations of the homogeneous expansion of quasi-convex mapping of order α defined on the polydisc in Cn and on the unit ball in a complex Banach space, respectively. 相似文献
6.
Z.V. Kovarik 《Linear algebra and its applications》1975,12(3):223-229
A continuation of [6]. Gershgorin-type estimates for spectra in Banach spaces and Hilbert spaces are established when the set of perturbations of a given operator is a line segment, a linear image of the unit operator ball on a Hilbert space, and a ball of operators on a Banach space. 相似文献
7.
Hongmin Ren 《Applied mathematics and computation》2009,213(2):440-448
In this paper, the upper and lower estimates of the radius of the convergence ball of the modified Newton’s method in Banach space are provided under the hypotheses that the Fréchet derivative of the nonlinear operator are center Hölder continuous for the initial point and the solution of the operator. The error analysis is given which matches the convergence order of the modified Newton’s method. The uniqueness ball of solution is also established. Numerical examples for validating the results are also provided, including a two point boundary value problem. 相似文献
8.
On the size of balls covered by analytic transformations 总被引:5,自引:0,他引:5
Prof. Lawrence A. Harris 《Monatshefte für Mathematik》1977,83(1):9-23
Two quantitative forms of the inverse function theorem giving estimates on the size of balls covered biholomorphically are proved for holomorphic mappings of a ball in a Banach space into the space. Also, a Bloch theorem forK-quasiconformal mappings on the open unit ball of a Banach space is given and some mapping properties ofK-quasiconformal mappings are deduced.Research supported by N. S. F. Grant GP-33117A-2. 相似文献
9.
复Banach空间中单位球上双全纯凸映射的偏差定理 总被引:1,自引:0,他引:1
本文讨论一般复Banach空间上单位球B的Caratheodory度量和Kobayashi 度量的性质,并据此将Cn(n≥1)中单位球Bn上双全纯凸映射的矩阵形式偏差定理 推广到一般复Banach空间的单位球B上. 相似文献
10.
J.C. Navarro-Pascual J.F. Mena-Jurado 《Journal of Mathematical Analysis and Applications》2008,339(1):719-734
We prove a new inequality valid in any two-dimensional normed space. As an application, it is shown that the identity mapping on the unit ball of an infinite-dimensional uniformly convex Banach space is the mean of n uniformly continuous retractions from the unit ball onto the unit sphere, for every n?3. This last result allows us to study the extremal structure of uniformly continuous function spaces valued in an infinite-dimensional uniformly convex Banach space. 相似文献
11.
?ukasz Piasecki 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(2):396-399
The unit sphere in an infinite dimensional Banach space is a lipschitzian retract of the unit ball. The aim of this paper is to present a new upper bound for the optimal retraction constant in some classical Banach spaces. In particular, an improved estimate from above is obtained for the space C[0,1]. 相似文献
12.
13.
Mark Elin 《Journal of Mathematical Analysis and Applications》2011,377(1):239-250
The Roper-Suffridge extension operator and its modifications are powerful tools to construct biholomorphic mappings with special geometric properties. The first purpose of this paper is to analyze common properties of different extension operators and to define an extension operator for biholomorphic mappings on the open unit ball of an arbitrary complex Banach space. The second purpose is to study extension operators for starlike, spirallike and convex in one direction mappings. In particular, we show that the extension of each spirallike mapping is A-spirallike for a variety of linear operators A. Our approach is based on a connection of special classes of biholomorphic mappings defined on the open unit ball of a complex Banach space with semigroups acting on this ball. 相似文献
14.
In this paper, a class of biholomorphic mappings named quasi-convex mapping of order α in the unit ball of a complex Banach space is introduced. When the Banach space is confined to ℂ
n
, we obtain the relation between this class of mappings and the convex mappings. Furthermore, the growth and covering theorems
of this class of mappings are given on the unit ball of a complex Banach space X. Finally, we get the second order terms coefficient estimations of the homogeneous expansion of quasi-convex mapping of order
α defined on the polydisc in ℂ
n
and on the unit ball in a complex Banach space, respectively.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
15.
We prove that a topological space is uniform Eberlein compact iff it is homeomorphic to a super weakly compact subset C of a Banach space such that the closed convex hull coC of C is super weakly compact. We also show that a Banach space X is super weakly compactly generated iff the dual unit ball BX* of X* in its weak star topology is affinely homeomorphic to a super weakly compactly convex subset of a Banach space. 相似文献
16.
准凸映照齐次展开式的精细估计 总被引:1,自引:0,他引:1
本文给出C~n中单位多圆柱上和复Banach空间中单位球上的准凸映照(含A型准凸映照和B型准凸映照)f齐次展开式的精细估计,其中x=0是f(x)-x的k 1阶零点.同时,还讨论了复Banach空间单位球上准凸映照的构造,它为准凸映照齐次展开式的精细估计提供极值映照. 相似文献
17.
Quantization consists in studying the L
r
-error induced by the approximation of a random vector X by a vector (quantized version) taking a finite number n of values. We investigate this problem for Gaussian random vectors in an infinite dimensional Banach space and in particular, for Gaussian processes. A precise link proved by Fehringer(4) and Dereich et al.
(3) relates lower and upper bounds for small ball probabilities with upper and lower bounds for the quantization error, respectively. We establish a complete relationship by showing that the same holds for the direction from the quantization error to small ball probabilities. This allows us to compute the exact rate of convergence to zero of the minimal L
r
-quantization error from logarithmic small ball asymptotics and vice versa. 相似文献
18.
范洪福 《应用泛函分析学报》2006,8(4):304-307
讨论向量值函数的Banach代数L∞(T;X)的极大理想空间的拓扑性质和代数性质,得到了若干结果;给出了Banach空间H∞(D;X)中闭单位球的端点的一条性质. 相似文献
19.
I. K. Argyros 《分析论及其应用》1993,9(1):1-9
We provide convergence results and error estimates for Newton-like methods in generalized Banach spaces. The idea of a generalized
norm is used whichis defined to be a map from a linear space into a partially ordered Banach space. Convergence results and
error estimates are improved compared with the real norm theory. 相似文献
20.
《复变函数与椭圆型方程》2012,57(4):291-301
In this paper, we obtain the growth result for normalized convex mappings on the unit ball of a complex Banach space. Also we give some bounds of coefficients and a distortion result for convex mappings on the unit ball of a complex Hilbert space. 相似文献