矩阵指数计算的广义极分解方法  

A Generalized Polar Decompositions Method for Matrix Exponential

作　　者：田益民[1] 

机构地区：[1]北京印刷学院,北京102600

出　　处：《北京印刷学院学报》2011年第2期62-63,共2页Journal of Beijing Institute of Graphic Communication

基　　金：北京市教委(PHR(IHLB)201107145);国家自然科学基金(F60850007);北京市自然科学基金(A1092012);北京印刷学院校科研重点(Ea-09-14)

摘　　要：李群算法是在流形上计算微分方程数值解的方法,其基本思想是把数值解限制在比平直的欧氏空间小而又比解流形大的流形上,这样从整体上会对算法有约束作用,使得数值解不会随着时间的增加而变得面目全非。虽然如此,李群算法有一个重大缺陷,当离散后得到的矩阵规模变大时,矩阵指数计算的计算量会迅速增大,从而严重影响了李群算法的应用。针对这一问题,讨论了提高计算矩阵指数运算速度的广义极分解方法。Lie group method is a kind of promissing method,its basic ideas is to keep the numeric solution in a manifold which is less than the Euclid space while bigger than the analytic solution manifold,so we can get more exact numeric solution than by other method.But there is a serious problem to use Lie group method,since we have to face the matrix exponential calculation and it will be more difficulty when the order of the matrix get big and big after discretion.So we discussed the generalized polar decompositions method for matrix exponential.

关 键 词：李群算法 指数运算 流形 广义极分解 

分 类 号：O175[理学—数学]