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

Hung-Yuan Fan, Eric King wah Chu

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3 Citations (Scopus)


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 A (or pencil A−λB). The engine of the method is the inversion of the matrix P2P2 A−γIn or Pl2Pl2 (A−γB), for some orthonormal P2 or Pl2 from Rn×(n−m), making use of the structures in A or A−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.

Original languageEnglish
Pages (from-to)70-86
Number of pages17
JournalJournal of Computational and Applied Mathematics
Publication statusPublished - 1 May 2017


  • Deflating subspace
  • Invariant subspace
  • Large-scale problem
  • Nonsymmetric algebraic Riccati equation
  • Sparse matrix
  • Sylvester equation

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