大学数学
大學數學
대학수학
COLLEGE MATHEMATICS
2011年
4期
93-98
,共6页
线性矩阵方程%迭代法%双对称解%最佳逼近解%最小二乘解
線性矩陣方程%迭代法%雙對稱解%最佳逼近解%最小二乘解
선성구진방정%질대법%쌍대칭해%최가핍근해%최소이승해
linear matrix equation%iterative method%bisymmetric solution%optimal approximation solution%least-squares solution
提出一种求解线性矩阵方程AX＋XB=C双对称解的迭代法.该算法能够自动地判断解的情况,并在方程相容时得到方程的双对称解,在方程不相容时得到方程的最小二乘双对称解.对任意的初始矩阵,在没有舍入误差的情况下,经过有限步迭代得到问题的一个双对称解.若取特殊的初始矩阵,则可以得到问题的极小范数双对称解,从而巧妙地解决了对给定矩阵求最佳逼近解的问题.
提齣一種求解線性矩陣方程AX＋XB=C雙對稱解的迭代法.該算法能夠自動地判斷解的情況,併在方程相容時得到方程的雙對稱解,在方程不相容時得到方程的最小二乘雙對稱解.對任意的初始矩陣,在沒有捨入誤差的情況下,經過有限步迭代得到問題的一箇雙對稱解.若取特殊的初始矩陣,則可以得到問題的極小範數雙對稱解,從而巧妙地解決瞭對給定矩陣求最佳逼近解的問題.
제출일충구해선성구진방정AX＋XB=C쌍대칭해적질대법.해산법능구자동지판단해적정황,병재방정상용시득도방정적쌍대칭해,재방정불상용시득도방정적최소이승쌍대칭해.대임의적초시구진,재몰유사입오차적정황하,경과유한보질대득도문제적일개쌍대칭해.약취특수적초시구진,칙가이득도문제적겁소범수쌍대칭해,종이교묘지해결료대급정구진구최가핍근해적문제.
An iterative method to find the bisymmetric solution of the linear matrix equation AX＋XB=C is put forward in this paper.This iterative method can judge automatically the information of solutions.When the equation is consistent,it converges a bisymmetric solution of the equation.When the equation is inconsistent,It converges the least-squares bisymmetric solution of the equation.For any initial matrix,a bisymmetric solution can be obtained within finite iteration steps in the absence of roundoff errors.If a special kind of initial matrix is chosen,the bisymmetric solution with least norm can be obtained,and wonderfully handle the problem of solving its optimal approximation solution for a given matrix.
