Numerical Study on Nonsymmetric Algebraic Riccati Equations

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• 作者：Changfeng Ma ; Huaize Lu
• 关键词：Nonsymmetric algebraic Riccati equation ; numerical iteration methods ; reducible singular M ; matrix ; regular M ; matrix ; minimal nonnegative solution
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：13
• 期：6
• 页码：4961-4973
• 全文大小：526 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454
• 卷排序：13

文摘

In this paper, we consider the nonsymmetric algebraic Riccati equation whose four coefficient matrices form an M-matrix K. When K is a regular M-matrix, the Riccati equation is known to have a minimal nonnegative solution. We present two new numerical methods which can be applied directly in the case where K is a regular M-matrix. Furthermore, we find that the alternately linearized implicit iteration method is also feasible. In addition, we study the monotone convergence property of the proposed methods. Numerical experiments show that the above three numerical iteration methods are feasible and effective for solving the nonsymmetric algebraic Riccati equation.