循环线性方程组的求解  

The Algorithm for Solving of Circulant Linear System

作　　者：沈光星[1] 黄德超[1] 

机构地区：[1]杭州师范学院数学与应用研究所,杭州310036

出　　处：《科技通报》2006年第3期283-287,共5页Bulletin of Science and Technology

基　　金：国家自然科学基金(10271037)

摘　　要：利用多项式矩阵理论,给出了循环线性方程组有解的判定并求出各种情况下的解。若方程组有唯一解,求出其唯一解;若方程组有无穷解,求出其极小范数解;若方程组无解,求出其极小范数最小二乘解。In this paper, the judgement of existing solution to circulant linear equations set and the solutions under all kinds of circumstances are presented by polynomial matrix theory. When the solution of equations is unique, unique solution is given;When the number of the solution of equations is infinite,mininum norm solution is solved; When the solutions of equations don＇t exist, the mininum norm least squares solution is solved.

关 键 词：计算数学 循环矩阵 行初等变换 MOORE-PENROSE逆 极小范数解 极小范数最小二乘解 

分 类 号：O151.2[理学—数学]