Projected nonsymmetric algebraic Riccati equations and refining estimates of invariant and deflating subspaces

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• 作者：Hung-Yuan Fan^a ; ^{hyfan@math.ntnu.edu.tw} ; Eric King-wah Chu^b ; ^{eric.chu@monash.edu}
• 关键词：15A18 ; 15A22 ; 15A24 ; 65F15 ; 65F50
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 May 2017
• 年：2017
• 卷：315
• 期：Complete
• 页码：70-86
• 全文大小：563 K
• 卷排序：315

文摘

We consider the numerical solution of the projected nonsymmetric algebraic Riccati equations or their associated Sylvester equations via Newton’s method, arising in the refinement of estimates of invariant (or deflating subspaces) for a large and sparse real matrix AA (or pencil A−λBA−λB). The engine of the method is the inversion of the matrix P2P2⊤A−γIn or Pl2Pl2⊤(A−γB), for some orthonormal P2P2 or Pl2Pl2 from Rn×(n−m)Rn×(n−m), making use of the structures in AA or A−λBA−λB and the Sherman–Morrison–Woodbury formula. Our algorithms are efficient, under appropriate assumptions, as shown in our error analysis and illustrated by numerical examples.