初等稳定矩阵约化A_(0)为上Hessenberg型的方法研究  

Research on Method of Reducing A_(0) to Upper Hessenberg Type with Elementary Stability Matrix

作　　者：苏尔[1] SU Er(College of Media Engineering,Communication University of Zhejiang,Hangzhou 310018,China)

机构地区：[1]浙江传媒学院媒体工程学院,杭州310018

出　　处：《计算机科学》2021年第S01期649-657,共9页Computer Science

摘　　要：文中讨论用初等矩阵技术选用部分主元素的Gauss消去法将A0约化变换为Hessenberg矩阵,为使数值具有稳定性,重视如何交换的本质性基础问题。首先简述概括了约化方法的矩阵算式;其次明确了递推约化运算规则式子形成的推演依据;然后重点详述展开约化方法的递推运算完全步骤和逻辑实现,清楚表述最后约化结果与矩阵算式准确计算结果一致事实;最后给出数值实例验证结论,约化方法基于充分计算依据并实际紧凑可行。This paper discusses how to reduce A_(0) to Hessenberg matrix by using Gauss elimination method of partial principal elements using elementary matrix technology.In order to make the numerical stability,the essential basic problem of how to exchange is emphasized.The first part briefly summarizes the matrix formula of reduction method.The second part further clarifies the basis of deducing the formula form of recursive reduction operation rule.The third part focuses on the details of recursive algorithm complete steps and logic implementation of the reduction method,and clearly states the fact that the final reduction result is consistent with the accurate calculation result of the matrix formula.The fourth part is a concrete example to verify the conclusion:the reduction method is based on sufficient calculation basis and is actually compact and feasible.

关 键 词：初等矩阵 行列交换 矩阵分块 递推约化 元素置换 约化矩阵 

分 类 号：O241.6[理学—计算数学]