On the eigenvalues and eigenvectors of block triangular preconditioned block matrices

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Block lower triangular matrices and block upper triangular matrices are popular preconditioners for $2\times 2$ block matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned matrices are related.
Original languageEnglish
Pages (from-to)517-525
Number of pages8
JournalSIAM Journal on Matrix Analysis and Applications
Early online date24 Apr 2014
Publication statusE-pub ahead of print - 24 Apr 2014


  • block triangluar preconditioner
  • convergence
  • eigenvalues
  • eigenvectors
  • iterative method
  • saddle point system

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