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1.
For a very general weight function, the equivalent conditions of complete convergence for weighted sums of independent but
not necessary identically distributed random variables are given. The previous situation of only sufficient results except
for particular weight functions is changed. These results may help deduce many known ones and bring to light richer content.
Project supported by the National Natural Science Foundation of China (Grant No. 19671078). the Natural Science Foundation
of the Highter Education Department of Cuangdong Province and the National Science Foundation of the Education Commission
of Jiangsu Province. 相似文献
2.
Since Rosen’s gradient projection method was published in 1960, a rigorous convergence proof of his method has remained an
open question. A convergence theorem is given in this paper.
Part of this author’s work was done while he studied at the Department of Mathematics, University of California at Santa Barbara,
and was supported by the National Science Foundation under Grant No. MCS83-14977.
Part of this author’s work was done while he visited the Computer Science Department, University of Minnesota, Minneapolis,
and was supported by the National Science Foundation under Grant No. MCS81-01214. 相似文献
3.
Smoothing Trust Region Methods for Nonlinear Complementarity Problems with P
0-Functions 总被引:1,自引:0,他引:1
By using the Fischer–Burmeister function to reformulate the nonlinear complementarity problem (NCP) as a system of semismooth
equations and using Kanzow’s smooth approximation function to construct the smooth operator, we propose a smoothing trust
region algorithm for solving the NCP with P
0 functions. We prove that every accumulation point of the sequence generated by the algorithm is a solution of the NCP. Under
a nonsingularity condition, local Q-superlinear/Q-quadratic convergence of the algorithm is established without the strict
complementarity condition.
This work was partially supported by the Research Grant Council of Hong Kong and the National Natural Science Foundation of
China (Grant 10171030). 相似文献
4.
Wei Cheng 《中国科学A辑(英文版)》2009,52(8):1796-1800
We obtain a partial generalization of Birkhoff’s theorem of invariant curve to higher dimesional case in the context of viscosity
solutions of Hamilton-Jacobi equations, or weak KAM theory. This is a new approach after Herman’s proof.
This work was supported by the National Basic Research Program of China (Grant No. 2007CB814800) and National Natural Science
Foundation of China (Grant No. 10301012) 相似文献
5.
It is proved that every proper holomorphic self-map of a smooth bounded Reinhardt domain in ℂ2 is an automorphism.
The first author’s work was supported in part by the National Natural Science Foundation of China (Grant No. 10571135) and
the Doctoral Program Foundation of the Ministry of Education of China (Grant No. 20050240711) 相似文献
6.
Some convergence results of one-leg methods for nonlinear neutral delay integro-differential equations (NDIDEs) are obtained.
It is proved that a one-leg method is E (or EB) -convergent of order p for nonlinear NDIDEs if and only if it is A-stable and consistent of order p in classical sense for ODEs, where p = 1, 2. A numerical example that confirms the theoretical results is given in the end of this paper.
This work was supported by National Natural Science Foundation of China (Grant No. 10871164), the Natural Science Foundation
of Hunan Province (Grant No. 08JJ6002), and the Scientific Research Fund of Changsha University of Science and Technology
(Grant No. 1004259) 相似文献
7.
In this paper, an unconstrained optimization method using the nonmonotone second order Goldstein’s line search is proposed.
By using the negative curvature information from the Hessian, the sequence generated is shown to converge to a stationary
point with the second order optimality conditions. Numerical tests on a set of standard test problems confirm the efficiency
of our new method.
This work was supported by the National Natural Science Foundation of China (Grant No. 10231060) and the Specialized Research
Fund of Doctoral Program of Higher Education of China (Grant No. 20040319003) 相似文献
8.
Q-Learning Algorithms with Random Truncation Bounds and Applications to Effective Parallel Computing
Motivated by an important problem of load balancing in parallel computing, this paper examines a modified algorithm to enhance
Q-learning methods, especially in asynchronous recursive procedures for self-adaptive load distribution at run-time. Unlike
the existing projection method that utilizes a fixed region, our algorithm employs a sequence of growing truncation bounds
to ensure the boundedness of the iterates. Convergence and rates of convergence of the proposed algorithm are established.
This class of algorithms has broad applications in signal processing, learning, financial engineering, and other related fields.
G. Yin’s research was supported in part by the National Science Foundation under Grants DMS-0603287 and DMS-0624849 and in
part by the National Security Agency under Grant MSPF-068-029.
C.Z. Xu’s research was supported in part by the National Science Foundation under Grants CCF-0611750, DMS-0624849, CNS-0702488,
and CRI-0708232.
L.Y. Wang’s research was supported in part by the National Science Foundation under Grants ECS-0329597 and DMS-0624849 and
by the Michigan Economic Development Council. 相似文献
9.
WenGuang Zhai 《中国科学A辑(英文版)》2009,52(5):857-874
In this paper we study the mean square of the error term in the Weyl’s law of an irrational (2l + 1)-dimensional Heisenberg manifold. An asymptotic formula is established.
This work was supported by National Natural Science Foundation of China (Grant No. 10771127) 相似文献
10.
For finding a root of a function f, Müler’s method is a root-finding algorithm using three values of f in every step. The natural values available are values of f and values of its first number of derivatives, called standard information. Based on standard information, we construct an
iteration method with maximal order of convergence. It is a natural generalization of Müller’s iteration method.
This work was partially supported by National Natural Science Foundation of China (Grant No. 10471128), NSFC (Grant No. 10731060). 相似文献
11.
Ke-jian Xu 《中国科学A辑(英文版)》2007,50(1):116-120
Based on the work of Lenstra, a succinct proof of Browkin’s conjecture about the elements of order five in K
2(ℚ) is given.
This work was supported by the National Natural Science Foundation of China (Grant No. 10371061). 相似文献
12.
Chang-jian Zhao 《中国科学A辑(英文版)》2007,50(9):1347-1360
In this paper, we first introduce a concept of L
p
-dual Quermassintegral sum function of convex bodies and establish the polar projection Minkowski inequality and the polar
projection Aleksandrov-Fenchel inequality for L
p
-dual Quermassintegral sums. Moreover, by using Lutwak’s width-integral of index i, we establish the L
p
-Brunn-Minkowski inequality for the polar mixed projection bodies. As applications, we prove some interrelated results.
This work was partially supported by the National Natural Science Foundation of China (Grant No. 10271071), Zhejiang Provincial
Natural Science Foundation of China (Grant No. Y605065) and Foundation of the Education Department of Zhejiang Province of
China (Grant No. 20050392) 相似文献
13.
Applying the Riemann-Roch theorem,we calculate the dimension of a kind of mero- morphicλ-differentials' space on compact Riemann surfaces.And we also construct a basis of theλ-differentials' space.As the main result,the Cauchy type of integral formula on compact Riemann surfaces is established. 相似文献
14.
The generalized Friedman’s urn model is a popular urn model which is widely used in many disciplines.In particular,it is extensively used in treatment allocation schemes in clinical trials.In this paper,we show that both the urn composition process and the allocation proportion process can be approximated by a multi-dimensional Gaussian process almost surely for a multi-color generalized Friedman’s urn model with both homogeneous and non-homogeneous generating matrices.The Gaussian process is a solution of ... 相似文献
15.
Jia Zhongxiao 《中国科学A辑(英文版)》1989,42(6):577-585
For classical orthogonal projection methods for large matrix eigenproblems, it may be much more difficult for a Ritz vector
to converge than for its corresponding Ritz value when the matrix in question is non-Hermitian. To this end, a class of new
refined orthogonal projection methods has been proposed. It is proved that in some sense each refined method is a composite
of two classical orthogonal projections, in which each refined approximate eigenvector is obtained by realizing a new one
of some Hermitian semipositive definite matrix onto the same subspace. Apriori error bounds on the refined approximate eigenvector are established in terms of the sine of acute angle of the normalized
eigenvector and the subspace involved. It is shown that the sufficient conditions for convergence of the refined vector and
that of the Ritz value are the same, so that the refined methods may be much more efficient than the classical ones.
Project supported by the China State Major Key Projects for Basic Researches, the National Natural Science Foundation of China
(Grant No. 19571014), the Doctoral Program (97014113), the Foundation of Excellent Young Scholors of Ministry of Education,
the Foundation of Returned Scholars of China and the Liaoning Province Natural Science Foundation. 相似文献
16.
LetΔ_1(x;φ) be the error term of the first Riesz mean of the Rankin-Selberg problem. We study the higher power moments ofΔ_1(x;φ) and derive an asymptotic formula for the 3-rd, 4-th and 5-th power moments by using Ivic's large value arguments and other techniques. 相似文献
17.
Convergence of Newton‘’s Method and Uniqueness of the Solution of Equations in Banach SpacesⅡ 总被引:7,自引:0,他引:7
XingHuaWANG ChongLI 《数学学报(英文版)》2003,19(2):405-412
Some results on convergence of Newton‘s method in Banach spaces are established under the assumption that the derivative of the opderators satisfies the radius or center Lipschitz condition with a weak L average. 相似文献
18.
Wenyu Sun Liusheng Hou Chuangying Dang 《Computational Optimization and Applications》2008,40(1):59-72
It is well-known that the conjugate gradient method is widely used for solving large scale optimization problems. In this
paper a modified trust-region method with Beale’s Preconditioned Conjugate Gradient (BPCG) technique is developed for solving
unconstrained optimization problems. The modified version adopts an adaptive rule and retains some useful information when
an unsuccessful iteration occurs, and therefore improves the efficiency of the method. The behavior and the convergence properties
are discussed. Some numerical experiments are reported.
This work was partially supported by Grant of the National Natural Science Foundation of China, Grant: 20040319003 of the
Doctoral Site of the Education Ministry of China, and SRG: 7001428 of City University of Hong Kong. 相似文献
19.
This paper investigates the asymptotic properties of the modified likelihood ratio statistic for testing homogeneity in bivariate normal mixture models with an unknown structural parameter. It is shown that the modified likelihood ratio statistic has χ22 null limiting distribution. 相似文献
20.
Qinian Jin 《中国科学A辑(英文版)》1999,42(11):1137-1146
Some converse and saturation results on Tikhonov regularization of nonlinear ill-posed problems are proved and the aposteriori parameter choice yielding optimal rates of convergence is discussed
Project supported by the National Natural Science Foundation of China (Grant No. 9801018). 相似文献