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71.
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
72.
Andrzej Kozek 《Journal of multivariate analysis》1977,7(1):89-106
A general method for obtaining inequalities of Cramér-Rao type for convex loss functions is presented. It is shown under rather weak assumptions that there are at least as many such inequalities as best unbiased estimators. More precisely, it is shown that an estimator is efficient with respect to an inequality of Cramér-Rao type if and only if it is the best in the class of unbiased estimators. Moreover, theorems of Blyth and Roberts (“Proceedings Sixth Berkeley Symposium on Math. Statist. Prob.,”) and of Blyth (Ann. Statist.2, 464–473) are extended. We make an use of methods of convex analysis and properties of convex integral functionals on Orlicz spaces. 相似文献
73.
An inexact Newton method is used to solve the steady, incompressible Navier–Stokes and energy equation. Finite volume differencing is employed on a staggered grid using the power law scheme of Patankar. Natural convection in an enclosed cavity is studied as the model problem. Two conjugate-gradient -like algorithms based upon the Lanczos biorthogonalization procedure are used to solve the linear systems arising on each Newton iteration. The first conjugate-gradient-like algorithm is the transpose-free quasi-minimal residual algorithm (TFQMR) and the second is the conjugate gradients squared algorithm (CGS). Incomplete lower-upper (ILU) factorization of the Jacobian matrix is used as a right preconditioner. The performance of the Newton- TFQMR algorithm is studied with regard to different choices for the TFQMR convergence criteria and the amount of fill-in allowed in the ILU factorization. Performance data are compared with results using the Newton-CGS algorithm and previous results using LINPACK banded Gaussian elimination (direct-Newton). The inexact Newton algorithms were found to be CPU competetive with the direct-Newton algorithm for the model problem considered. Among the inexact Newton algorithms, Newton-CGS outperformed Newton- TFQMR with regard to CPU time but was less robust because of the sometimes erratic CGS convergence behaviour. 相似文献
74.
The first, highly efficient conjugate addition of azide ion to α,β-unsaturated carbonyl compounds promoted by the simple recyclable ionic liquids, bmimPF6 and bmimBF4, are described. 相似文献
75.
In this paper we propose a new line search algorithm that ensures global convergence of the Polak-Ribière conjugate gradient
method for the unconstrained minimization of nonconvex differentiable functions. In particular, we show that with this line
search every limit point produced by the Polak-Ribière iteration is a stationary point of the objective function. Moreover,
we define adaptive rules for the choice of the parameters in a way that the first stationary point along a search direction
can be eventually accepted when the algorithm is converging to a minimum point with positive definite Hessian matrix. Under
strong convexity assumptions, the known global convergence results can be reobtained as a special case. From a computational
point of view, we may expect that an algorithm incorporating the step-size acceptance rules proposed here will retain the
same good features of the Polak-Ribière method, while avoiding pathological situations.
This research was supported by Agenzia Spaziale Italiana, Rome, Italy. 相似文献
76.
Bin Meng Maozheng Guo Xiaohong Cao 《Proceedings of the American Mathematical Society》2005,133(10):3087-3096
We introduce the operator-valued free Fisher information for a random variable in an operator-valued noncommutative probability space and point out its relations to the amalgamated freeness. Using M. Frank and D. Larson's modular frame notion we can construct the conjugate variable for an operator-valued semicircle variable with conditional expectation covariance. Then we obtain its free Fisher information and show it is equal to the index of the conditional expectation. At last the conjugate variable with respect to a modular frame operator for a semicircle variable is also constructed.
77.
褚玉明 《数学物理学报(B辑英文版)》2005,25(3):492-504
The main aim of this paper is to discuss the following two problems:λm)∈Hm×m, find A ∈ BSH≥n×n such that AX= X∧, where BSH≥n×n denotes the set of all n × n quaternion matrices which are bi-self-conjugate and nonnegative definite.Problem Ⅱ:Given B ∈ Hn×m, find -B∈SE such that ||B- B||Q = minA∈sE ||B - A||Q,necessary and sufficient conditions for SE being nonempty are obtained. The general form of elements in SE and the expression of the unique solution B of problem Ⅱ are given. 相似文献
78.
79.
Wang Xiangru Xiong Caidong Wen Xia Qiu Qi Luo Juanyan Deng Hao Xie Wen 《Optics Communications》2010,283(1):44-48
With the purpose of uniform gain coefficient along the axial direction in the core of gain guided and index anti-guided fiber, a new kind of side-pump scheme by wrapping particularly treated fibers around the central GGIAG fiber is reported in this paper. According to leakage mode analysis on wrapped fiber and numerical simulation on this pumping structure having ytterbium doped central fiber and conventional wrapped side fiber, we find this kind of pump scheme can improve the uniformity of gain coefficient along the fiber direction, and also, it can support multi channels of pumping sources by adding more side fibers to improve the total effective incident pumping power. 相似文献
80.
约束矩阵方程求解是指在满足一定约束条件下求矩阵方程(组)的解.在子空间约束条件下,利用共轭梯度法,结合线性投影算子,得到矩阵方程ATXB+BTXTA=D的解,进一步得到其最佳逼近.最后用数值例子证实了算法的有效性. 相似文献