[1]陈凤坤,雷秀仁. 一种求解病态复线性方程组的混合算法[J].计算机技术与发展,2017,27(05):16-19.
　CHEN Feng-kun,LEI Xiu-ren. A Hybrid Algorithm of Ill-conditioned Complex Linear Equations[J].,2017,27(05):16-19.
点击复制

 一种求解病态复线性方程组的混合算法()
分享到：

《计算机技术与发展》[ISSN:1006-6977/CN:61-1281/TN]

卷:
27
期数:
2017年05期
页码:
16-19
栏目:
智能、算法、系统工程
出版日期:
2017-05-10

文章信息/Info

Title:
 A Hybrid Algorithm of Ill-conditioned Complex Linear Equations
文章编号:
1673-629X（2017)05-0016-04
作者:
 陈凤坤; 雷秀仁
 华南理工大学 数学学院
Author(s):
 CHEN Feng-kun; LEI Xiu-ren
关键词:
 ; 病态复线性方程组; 模拟退火算法; 双共轭梯度法; 混合算法; 希尔伯特矩阵
Keywords:
 ; ill-conditioned complex linear equations; simulated annealing algorithm; bi-conjugate gradient algorithm;  hybrid algorithm; Hilbert matrix
分类号:
O24
文献标志码:
A
摘要:
 病态复线性方程的求解是现代应用数学和很多工程应用面临的难题,用一般算法进行求解时,得到的误差较大,因此在一些高精度的工程应用上,其结果往往不是特别理想.而随着科技的发展,现代很多工程应用对数据具有越来越高的精度要求(尤其是国家航天航空),因此一个能求解病态复线性方程组的高精度算法是很有必要的.从病态复线性方程组求解的特点出发,对模拟退火法进行改进,并将其全局的收敛能力与双共轭梯度法的高精度求解能力结合起来,提出了一种BCG-SA混合算法.数据实验表明,模拟退火法能对双共轭梯度法求出的解进行微调动,帮助双共轭梯度法在概率意义上跳出局部极小值点,从而提高求解精度.
Abstract:
 Solving ill-conditioned complex linear equations is difficult in modern applied mathematics and many engineering application,and it is easy to produce significant error and bad result for general algorithms in some high-accuracy application with a usual algorithm.With the development of science and technology,there is more and more restrictions on data accuracy for modern industry especially space flight and aviation.Therefore,it is necessary and impending to find a high accuracy algorithm for ill-conditioned complex linear equations.According to the characteristics of ill-conditioned complex linear equations,a hybrid algorithm of BCG-SA improved with simulated annealing algorithm has been proposed with the advantages of global convergence and high precision solution for bi-conjugate gradient algorithm.The experimental results show that the hybrid algorithm has promoted the precision of solution for bi-conjugate gradient algorithm which can jump out of the neighborhoods of local minimum points in the sense of probability.

相似文献/References:

[1]张志宏,吴庆波,邵立松,等.基于飞腾平台TOE协议栈的设计与实现[J].计算机技术与发展,2014,24(07):1.
　ZHANG Zhi-hong,WU Qing-bo,SHAO Li-song,et al. Design and Implementation of TCP/IP Offload Engine Protocol Stack Based on FT Platform[J].,2014,24(05):1.
[2]梁文快,李毅. 改进的基因表达算法对航班优化排序问题研究[J].计算机技术与发展,2014,24(07):5.
　LIANG Wen-kuai,LI Yi. Research on Optimization of Flight Scheduling Problem Based on Improved Gene Expression Algorithm[J].,2014,24(05):5.
[3]黄静,王枫,谢志新,等. EAST文档管理系统的设计与实现[J].计算机技术与发展,2014,24(07):13.
　HUANG Jing,WANG Feng,XIE Zhi-xin,et al. Design and Implementation of EAST Document Management System[J].,2014,24(05):13.
[4]侯善江[],张代远[][][]. 基于样条权函数神经网络P2P流量识别方法[J].计算机技术与发展,2014,24(07):21.
　HOU Shan-jiang[],ZHANG Dai-yuan[][][]. P2P Traffic Identification Based on Spline Weight Function Neural Network[J].,2014,24(05):21.
[5]李璨,耿国华,李康,等. 一种基于三维模型的文物碎片线图生成方法[J].计算机技术与发展,2014,24(07):25.
　LI Can,GENG Guo-hua,LI Kang,et al. A Method of Obtaining Cultural Debris’ s Line Chart Based on Three-dimensional Model[J].,2014,24(05):25.
[6]翁鹤,皮德常. 混沌RBF神经网络异常检测算法[J].计算机技术与发展,2014,24(07):29.
　WENG He,PI De-chang. Chaotic RBF Neural Network Anomaly Detection Algorithm[J].,2014,24(05):29.
[7]刘茜[],荆晓远[],李文倩[],等. 基于流形学习的正交稀疏保留投影[J].计算机技术与发展,2014,24(07):34.
　LIU Qian[],JING Xiao-yuan[,LI Wen-qian[],et al. Orthogonal Sparsity Preserving Projections Based on Manifold Learning[J].,2014,24(05):34.
[8]尚福华,李想,巩淼. 基于模糊框架-产生式知识表示及推理研究[J].计算机技术与发展,2014,24(07):38.
　SHANG Fu-hua,LI Xiang,GONG Miao. Research on Knowledge Representation and Inference Based on Fuzzy Framework-production[J].,2014,24(05):38.
[9]叶偲,李良福,肖樟树. 一种去除运动目标重影的图像镶嵌方法研究[J].计算机技术与发展,2014,24(07):43.
　YE Si,LI Liang-fu,XIAO Zhang-shu. Research of an Image Mosaic Method for Removing Ghost of Moving Targets[J].,2014,24(05):43.
[10]余松平[][],蔡志平[],吴建进[],等. GSM-R信令监测选择录音系统设计与实现[J].计算机技术与发展,2014,24(07):47.
　YU Song-ping[][],CAI Zhi-ping[] WU Jian-jin[],GU Feng-zhi[]. Design and Implementation of an Optional Voice Recording System Based on GSM-R Signaling Monitoring[J].,2014,24(05):47.

更新日期/Last Update: 2017-07-06