基于二阶系统解耦对非奇异解的研究  

Research on nonsingular solution of AX + XB = 0 equation based on quadratic system decoupling

作　　者：张善美[1] 许峰[1] 

机构地区：[1]安徽理工大学理学院,安徽淮南232000

出　　处：《哈尔滨商业大学学报（自然科学版）》2014年第5期626-630,635,共6页Journal of Harbin University of Commerce：Natural Sciences Edition

摘　　要：对求解齐次AX+XB=0方程非奇异解的研究,可以有效解决二阶系统解耦问题.但高阶系统无法通过正常的计算方法找到非奇异解,而且误差很高.针对由二阶系统变形来的AX+XB=0方程,并对其具有的特殊形式进行研究探讨,找到解的构造方法,从而更加准确的找到其非奇异解,将二阶系统进行有效的解耦,数值试验证明了该方法的可行性.The research of nonsingular solution of the AX＋XB=0 equation solution can ef-fectively solve the decoupling problem of second order system .However , high-order system cannot find the singular solution through the calculation method of normal , and the error is very high .In this paper , by the deformation to the equation of second order system with spe-cial form of research , the solution of the method was found , which was more accurate to find the singular solution , and effectively decouple the second -order system.The results of nu-merical experiments showed this constitution method was a feasible one , which supplied a simple approach for nonsingular solution of the Sylvester equation .

关 键 词：二阶系统 AX+XB=0方程 非奇异解 系统解耦 

分 类 号：O29[理学—应用数学]