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131.
Kunio Tanabe 《Annals of the Institute of Statistical Mathematics》1985,37(1):173-187
Summary The conjugate gradient method is developed for computing stationary probability vectors of a large sparse stochastic matrixP, which often arises in the analysis of queueing system. When unit vectors are chosen as the initial vectors, the iterative
method generates all the extremal probability vectors of the convex set formed by all the stationary probability vectors ofP, which are expressed in terms of the Moore-Penrose inverse of the matrix (P−I). A numerical method is given also for classifying the states of the Markov chain defined byP. One particular advantage of this method is to handle a very large scale problem without resorting to any special form ofP.
The Institute of Statistical Mathematics 相似文献
132.
在给出块共轭概念的基础上,提出了适合并行计算的向量组的块共轭化方法,进而得到解无约束最优化问题的并行块共轭方向法.有大量数值结果表明块共轭方向法具有工作量少.适用函数范围广等特点,是一种比较有效的无约束最优化方法. 相似文献
133.
134.
Jianye Lu Zuochun Shen Yanzhou Zhou Yunhua Dong Huide Gao Zuguang Ma 《Optics and Lasers in Engineering》2004,41(2):289-295
A new method of coherent summation of laser beams is proposed. Two-dimension numerical simulation based on the conjugate gradient algorithm shows that the combination efficiency is about 94.8%, and an error less than 2.4% with a 16-level phase quantized diffraction optical element. Error analysis has also been performed. 相似文献
135.
David F. Shanno 《Mathematical Programming》1985,33(1):61-67
The paper examines a method of implementing an angle test for determining when to restart conjugate gradient methods in a steepest descent direction. The test is based on guaranteeing that the cosine of the angle between the search direction and the negative gradient is within a constant multiple of the cosine of the angle between the Fletcher-Reeves search direction and the negative gradient. This guarantees convergence, for the Fletcher-Reeves method is known to converge. Numerical results indicate little, if anything, is lost in efficiency, and indicate gains may well be possible for large problems. 相似文献
136.
Ákos Szilágyi 《Tetrahedron letters》2004,45(22):4307-4309
A simple synthesis of 1,2-dithiolan-3-ones from α,β-unsaturated thiophenyl esters has been elaborated. With the aim of introducing the biologically active 1,2-dithiolan-3-one-1-oxide moiety of leinamycin into a nucleoside, the method was successfully applied to thymidine-5′-aldehyde. 相似文献
137.
Wu Li 《Mathematical Programming》1996,72(1):17-32
In this paper, we show that an analogue of the classical conjugate gradient method converges linearly when applied to solving
the problem of unconstrained minimization of a strictly convex quadratic spline. Since a strictly convex quadratic program
with simple bound constraints can be reformulated as unconstrained minimization of a strictly convex quadratic spline, the
conjugate gradient method is used to solve the unconstrained reformulation and find the solution of the original quadratic
program. In particular, if the solution of the original quadratic program is nondegenerate, then the conjugate gradient method
finds the solution in a finite number of iterations.
This author's research is partially supported by the NASA/Langley Research Center under grant NCC-1-68 Supplement-15. 相似文献
138.
In order to reduce the cost of large three-dimensional calculations of steady state free surfaces, we have combined a time-dependent approach, a decoupling algorithm and a conjugate gradient solver along the lines introduced earlier by Gresho and Chan. The free surface is calculated separately by applying the kinematic condition to a number of faces defined on the undeformed surface. For the pseudo-time-marching technique we show that it is economical to adopt different time steps for the free surface calculation and the other fields. The accuracy of the method is tested on the well-known circular die problem; the method is then used to reveal the effects of inertia and shear thinning on square and rectangular dies. 相似文献
139.
140.
Attempts to convert a propargylic alcohol bearing an imidazolone substituent to the corresponding aldehyde under Parikh-Doering conditions gave an α,β-unsaturated-β-methylsulfanyl aldehyde, which cyclised under mildly acidic conditions. 相似文献