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AJA Outstanding Paper Award of 2023

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Asian Journal of Andrology 2024年第3期26卷 I0003-I0004页

关键词： vitamin parameters aitken

Higher Order aitken Extrapolation with Application to Converging and Diverging Gauss-Seidel Iterations

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Journal of Applied Mathematics and Physics 2013年第5期1卷 128-143页

作者： Ababu Teklemariam Tiruneh Department of Environmental Health Science University of Swaziland Mbabane Swaziland

In this paper, aitken’s extrapolation normally applied to convergent fixed point iteration is extended to extrapolate the solution of a divergent iteration. In addition, higher order aitken extrapolation is introduced that enables successive decomposition of high Eigen values of the iteration matrix to enable convergence. While extrapolation of a convergent fixed point iteration using a geometric series sum is a known form of aitken acceleration, it is shown that in this paper, the same formula can be used to estimate the solution of sets of linear equations from diverging Gauss-Seidel iterations. In both convergent and divergent iterations, the ratios of differences among the consecutive values of iteration eventually form a convergent (divergent) series with a factor equal to the largest Eigen value of the iteration matrix. Higher order aitken extrapolation is shown to eliminate the influence of dominant Eigen values of the iteration matrix in successive order until the iteration is determined by the lowest possible Eigen values. For the convergent part of the Gauss-Seidel iteration, further acceleration is made possible by coupling of the extrapolation technique with the successive over relaxation (SOR) method. Application examples from both convergent and divergent iterations have been provided. Coupling of the extrapolation with the SOR technique is also illustrated for a steady state two dimensional heat flow problem which was solved using MATLAB programming.

关键词： Linear Equations Gauss-Seidel Iteration aitken Extrapolation Acceleration Technique Iteration Matrix Fixed Point Iteration

加速微种群遗传算法及其在结构优化设计中的应用

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应用基础与工程科学学报 2008年第5期16卷 741-748页

作者：孙林松张伟华扬州大学水利科学与工程学院江苏扬州225009 海门市水利局堤防管理所江苏海门226100

将微种群遗传算法与基于启发式模式移动的局部寻优方法和aitken Δ^2加速策略相结合，给出了一种加速微种群遗传算法．算法中利用aitken Δ^2加速策略改进当前种群，利用基于启发式模式移动的局部寻优方法改进子代群体．利用3个数值优... 详细信息

将微种群遗传算法与基于启发式模式移动的局部寻优方法和aitken Δ^2加速策略相结合，给出了一种加速微种群遗传算法．算法中利用aitken Δ^2加速策略改进当前种群，利用基于启发式模式移动的局部寻优方法改进子代群体．利用3个数值优化算例测试了算法的性能，表明本文算法具有较好的收敛性和计算效率．最后将其用于桁架结构截面优化设计，10杆平面桁架和25杆空间桁架的优化结果表明，本文算法的计算精度和计算工作量均优于传统的遗传算法．

关键词：微种群遗传算法 aitken Δ^2加速局部寻优桁架优化

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aitken插值法在物理实验中的应用

物理实验 1987年第4期 168-171页

作者：刘希明董凡山东大学物理系

物理实验所测量的数据总是有限的,而实际上需要求出对于这些有限次测量以外的数据,或根据有限次测量结果做出一条光滑曲线或曲面,使其通过或尽可能靠近这些点,实验中变量之间的函数往往比较复杂而不便于计算或处理,甚至函数关系没有明... 详细信息

物理实验所测量的数据总是有限的,而实际上需要求出对于这些有限次测量以外的数据,或根据有限次测量结果做出一条光滑曲线或曲面,使其通过或尽可能靠近这些点,实验中变量之间的函数往往比较复杂而不便于计算或处理,甚至函数关系没有明显的解析表达式,需要根据有限次测量结果,对所研究问题中的函数关系建立一个简单的便于计算和处理的近似表达式,或寻找变量间的经验公式.解决这些问题最常用的是插值与曲线拟合等方法.

关键词：插值法数值分析线性插值 aitken 插值公式数学公式物理实验

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aitken序列和Fibonacci数

中等数学 1986年第5期 22-24+38页

作者：吴之季安徽省教育科学研究所

1.引言若干年前,我发现如果把 aitken 加速法应用于山下式所定义的序列(x):x=1+1/(x)且 x=1 (1)那么,得到的 aitken 序列(x~*)满足简单关系:x~*=x(2)表1给出了序列(x)与(x~*)的最初几个数值,这里

关键词：加速法 aitken Fibonacci

Extremity and extremital replantation

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外科研究与新技术 2009年第3期 178-180页

209360 Treatment of type C intercondylar fractures of distal humerus using dual plating/Liu Yake(刘雅克,Dept Orthop,Affil Hosp Nantong Univ,Nantong 226001)…∥Chin J Surg.-2009,47(12).-892～895Objective To evaluate the clinical outcome of dual plating in the treatment of humeral intercondylar type-C fractures in adults.Methods From June 2004 to October 2007,38 cases of type-C distal humeral fractures were stabilised with dual plating.There were 21 males and 17 females.The average age was 43 years with a range from 21 to 71 years.According to the AO classification,9 cases were of type C1,17 of C2 and 12 of C3.The posterior midline approach was selected.Twenty-one cases were exposed through the trans-olecranon osteotomy,11 through the Campbell (Van Gorder)approach,6 through triceps sparing approach.Autogenous bone graft was performed in 5 cases due to severe comminution.Results Thirty-five patients were followed-up for 14-30 months(mean 24.2 months).At the latest follow-up,the elbow flexion averaged 119°(range 90°-135°),and the loss of extension averaged 16.2° (range 5°-25°).All the patients got bony healing,the average healing period was 14 weeks.The patients were evaluated using the criteria of aitken and Rorabeek and the scores were 13 excellent,16 good,6 fair.Twenty-nine patients(82.9%)had a good or excellent results.Complications included 4 cases of traumatic osteoarthritis,2 heterotopic ossification,1 ulnar neuropathy.Infection as well as loosening or breakage of the implant was not found.Conclusion The dual plating is able to provide rigid fixation for the humeral intercondylar fractures.In addition,it can allow early functional exercise after operation,decrease the related complications significantly,and improve the functional results.13 refs,1 fig,1 tab.

关键词： ossification aitken breakage plating heterotopic distal neuropathy implant graft Infection

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THE BUZZ

城市漫步（GBA版） 2019年第2期 10-11页

RANDOM NUMBER 2,500 kilometers That's the diameter of the South Pole-aitken basin on the moon's far side,the site where the Chang'e-4 probe successfully landed last month.The exploratory vehicle was built by the China National Space Administration(CNSA)and made history on January 3 when it became the first man-made object to touch down on the far side of the moon.

关键词： touch aitken kilometer

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THE BUZZ

城市漫步（上海版、英文） 2019年第2期 8-9页

RANDOM NUMBER 2,500 kilometers That's the diameter of the South Pole-aitken basin on the moons far side,the site where the Chang'e-4 probe successfully landed last month.The exploratory vehicle was built by the China National Space Administration(CNSA)and made history on January 3 when it became the first manmade object to touch down on the far side of the moon.

关键词： manmade touch aitken

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样条函数在经济技术数学模型中的应用

北京市经济管理干部学院学报 1989年第2期4卷 39-45页

作者：金炳福

笔者在贵刊上发表的题为《数值逼近在经济技术数学模型中的应用》一文中,曾就某经济问题向读者较详细地介绍了Lagrange(拉格朗日)、aitken (埃特金)、Newten (牛顿)插值法,并指出交错使用三种方法的优越性。同时指出,它们的最大缺点是... 详细信息

笔者在贵刊上发表的题为《数值逼近在经济技术数学模型中的应用》一文中,曾就某经济问题向读者较详细地介绍了Lagrange(拉格朗日)、aitken (埃特金)、Newten (牛顿)插值法,并指出交错使用三种方法的优越性。同时指出,它们的最大缺点是当数据很多时,采用上述三种方法所建立起来的插值多项式次数高、计算较为复杂、稳定性差。并建议采用样条插值法去克服上述问题。本文将介绍如何采用样条函数去解决这一问题的。

关键词：样条函数样条插值数学模型插值多项式插值点 aitken 数值逼近简便性模型精度连续导数

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