引用本文:王大海.快速求解Lyapunov矩阵代数方程AтX+XA=-Q的Schawarz形法[J].控制理论与应用,1985,2(4):10~20.[点击复制]
Wang Dahai.THE SCHWARZ -FORM -METHOD FOR THE FAST SOLUTION OF LYAPUNOV MATRIX ALGEBRAIC EQUATION AтX+XA=-Q[J].Control Theory and Technology,1985,2(4):10~20.[点击复制]
快速求解Lyapunov矩阵代数方程AтX+XA=-Q的Schawarz形法
THE SCHWARZ -FORM -METHOD FOR THE FAST SOLUTION OF LYAPUNOV MATRIX ALGEBRAIC EQUATION AтX+XA=-Q
摘要点击 800  全文点击 385  投稿时间：1983-10-31  修订日期：1984-09-19
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DOI编号  
  1985,2(4):10-20
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英文关键词  
基金项目  
作者单位
王大海 北京航空学院 
中文摘要
      本文把矩阵A相似变换为Schawarz形，得到了快速求解Lyapunov矩阵代数方程AтX+XA=-Q的一种新算法——Schawarz形法。该法只需12.5n3+O（n2）次乘除运算，3.5n2+ O(n)个存贮单元，比现有文献提供的算法要求的乘除次数与存贮单元均降低了几个数量级。用Schawarz形法还可以判断矩阵A的渐近稳定性。
英文摘要
      In this paper, by similar transforming the matrix A to Schawarz-form,a new method for the fast solution of the Lyapunov matrix algebraic equation AтX+XA=-Q was developed which is called the Schawarz -form -metho(SFM). It needs only 12.5n3+O（n2）multiplication and/or division, and 3.5n2+O(n) memory bytes. This is less than that was required before by several orders. This method applies to also to the determination of the stability of the matrix A.