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A direct algorithm Maple Package of One-Dimensional Optimal System for Group Invariant Solutions

Communications in Theoretical Physics 2018年第1期69卷 14-22页

作者： Lin Zhang Zhong Han Yong Chen Shanghai Key Laboratory of Trustworthy Computing East China Normal UniversityShanghai 200062China Department of Physics Zhejiang Normal UniversityJinhua 321004China

To construct the one-dimensional optimal system of finite dimensional Lie algebra automatically,we develop a new Maple package One Optimal ***,we propose a new method to calculate the adjoint transformation matrix and find all the invariants of Lie algebra in spite of Killing form checking possible constraints of each ***,a new conception called invariance set is ***,this Maple package is proved to be more efficiency and precise than before by applying it to some classic examples.

关键词： symbolic computation mathematics mechanization direct algorithm optimal system

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RESEARCH OF PROBLEMS ON REALIZING direct algorithm OF WAVELET TRANSFORM

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Chinese Journal of Mechanical Engineering 2003年第2期16卷 136-140页

作者： Tang BaopingZhong YoumingQin ShurenDepartment of Mechanical Engineering,Chongqing University,Chongqing 400044, China Department of Mechanical Engineering Chongqing University 重庆 400044

direct algorithm of wavelet transform (WT) is the numerical algorithmobtained from the integral formula of WT by directly digitization. Some problems on realizing thealgorithm are studied. Some conclusions on the direct algorithm of discrete wavelet transform (DWT),such as discrete convolution operation formula of wavelet coefficients and wavelet components,sampling principle and technology to wavelets, deciding method for scale range of wavelets, measuresto solve edge effect problem, etc, are obtained. The realization of direct algorithm of continuouswavelet transform (CWT) is also studied. The computing cost of direct algorithm and Mallat algorithmof DWT are still studied, and the computing formulae are obtained. These works are beneficial todeeply understand WT and Mallat algorithm. Examples in the end show that direct algorithm can alsobe applied widely.

关键词： wavelet transform direct algorithm mallat algorithm

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A direct algorithm for Solving Singular LQ Optimal Control Problems

A Direct Algorithm for Solving Singular LQ Optimal Control P...

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第25届中国控制会议

作者： Zhang Pingjian, Xi Jianqing School of Computer Science and Technology, South China University of Technology, Guangzhou 510641

＜正＞Considered in this paper are the singular linear quadratic optimal control problems. A direct, constructive algorithm for solving this kind of problems is proposed. Compared to existing iterative algorithms, the new one terminates in finite steps and can obtain an analytic form for the value function. Compared to geometric approaches, the transformations involved in the new algorithm are straightforward and easy to apply. Numerical experiments demonstrate the validity of the proposed direct algorithm.

关键词： Singular controls LQ optimal control direct algorithm

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A Unified Approach Toward Simulating Constant and Varying Amplitude Fatigue Failure Effects of Metals with Fast and Efficient algorithms

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Acta Mechanica Solida Sinica 2021年第1期34卷 53-64页

作者： Si-Yu Wang Lin Zhan Hui-Feng Xi Heng Xiao College of Mechanics and Construction Engineering and MOE Key Lab of Disaster Forecast and Control in Engineering Jinan UniversityGuangzhou510632China

A new finite strain elastoplastic J2-flow model is established with an explicit formulation of work-hardening and softening effects up to eventual failure,in which both a new flow rule free of yielding and an asymptotically vanishing stress limit are *** novelties of this new model are as follows:(i)Fatigue failure effects under repeated loading conditions with either constant or varying amplitudes are automatically characterized as inherent response features;(ii)neither additional damage-like variables nor failure criteria need to be involved;and(iii)both high-and low-cycle fatigue effects may be simultaneously treated.A fast and efficient algorithm of high accuracy is proposed for directly simulating high-and medium-high-cycle fatigue failure effects under repeated loading *** this goal,a direct and explicit relationship between the fatigue life and the stress amplitude is obtained by means of explicit and direct procedures of integrating the coupled elastoplastic rate equations for any given number of loading-unloading cycles with varying stress *** examples suggest that the new algorithm is much more fast and efficient than usual tedious and very time-consuming integration procedures.

关键词： Metals Finite strain Elastoplasticity Fatigue failure direct algorithm

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GAUSSIAN PIVOTING METHOD FORSOLVING LINEAR COMPLEMENTARITY PROBLEM

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Applied Mathematics(A Journal of Chinese Universities) 1997年第4期12卷 419-426页

作者： L1DONGHUI ZengJinping Zhangzhongzhi DepertmentofAppliedMathematics HunanUniversityChangsha410082

In this paper, a new direct algorithm for solving linear complementarity problem with Z-matrix is proposed. The algorithm exhibits either a solution or its nonexistence after at most n steps (where n is the dimension ... 详细信息

关键词： Computational complexity direct algorithm Least solution Linear complementarity problem Z-matrix

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隐函救最小二乘曲线拟合的直接算法

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厦门大学学报(自然科学版) 1987年第5期 627-630页

作者：陈昆厦门大学物理学系

达到的小.式中N为观测点的总数,W1为权重因子,y为因变量,m代表测量值,c代表计算值。当待拟合的函数为显式函数时,y1c可由如下解析表达式直接算得

关键词： Curve fitting direct algorithm Implicit function Objec tive function

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