陕西科技大学学报(自然科学版)
陝西科技大學學報(自然科學版)
협서과기대학학보(자연과학판)
JOURNAL OF SHAANXI UNIVERSITY OF SCIENCE & TECHNOLOGY
2015年
1期
175-178,183
,共5页
线性矩阵方程%雅可比迭代法%收敛性%方阵乘幂求和法
線性矩陣方程%雅可比迭代法%收斂性%方陣乘冪求和法
선성구진방정%아가비질대법%수렴성%방진승멱구화법
linear matrix equations%Jacobi iterative method%convergence%summation of square matrix′s power (SSMP)
在很多问题中会遇到线性矩阵方程的求解问题,如果线性矩阵方程用矩阵直积和矩阵按行或按列进行拉直,用向量表示未知数不仅不方便,而且占用空间较大,因此有必要讨论线性矩阵方程的数值求解方法。本文给出了线性矩阵方程的迭代求解方法,讨论了迭代方法收敛的条件,给出了线性矩阵方程的雅可比迭代方法和方阵乘幂求和方法,用数值例子基于M at‐lab程序验证了算法的可行性。
在很多問題中會遇到線性矩陣方程的求解問題,如果線性矩陣方程用矩陣直積和矩陣按行或按列進行拉直,用嚮量錶示未知數不僅不方便,而且佔用空間較大,因此有必要討論線性矩陣方程的數值求解方法。本文給齣瞭線性矩陣方程的迭代求解方法,討論瞭迭代方法收斂的條件,給齣瞭線性矩陣方程的雅可比迭代方法和方陣乘冪求和方法,用數值例子基于M at‐lab程序驗證瞭算法的可行性。
재흔다문제중회우도선성구진방정적구해문제,여과선성구진방정용구진직적화구진안행혹안렬진행랍직,용향량표시미지수불부불방편,이차점용공간교대,인차유필요토론선성구진방정적수치구해방법。본문급출료선성구진방정적질대구해방법,토론료질대방법수렴적조건,급출료선성구진방정적아가비질대방법화방진승멱구화방법,용수치례자기우M at‐lab정서험증료산법적가행성。
We often encounter the problem of solving linear matrix equations in a number of situations such as Kronecker product and transform a matrix by line or by column into a vec‐tor .It is inconvenient to represent unknown variables with a vector and it will occupy a large space inevitable .Therefore ,it is very necessary to search the solution of linear matrix equa‐tions .In this paper ,we formulate an iterative procedure to solve linear matrix equations ,dis‐cuss the convergence condition of our iterative procedure and present the Jacobi method and the summation of square matrix′s power of linear matrix equations .Numerical experiments based on Matlab show the effectiveness of the proposed algorithm .