Analysis of augmented Krylov subspace methods

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Abstract

Residual norm estimates are derived for a general class of methods based on projection techniques on subspaces of the form Km + W, where K1n is the standard Krylov subspace associated with the original linear system and W is some other subspace. These '"augmented Krylov subspace methods" include eigenvalue deflation techniques as well as block-Krylov methods. Residual bounds are established which suggest a convergence rate similar to one obtained by removing the components of the initial residual vector associated with the eigenvalues closest to zero. Both the symmetric and nonsynimetric cases are analyzed.

Original languageEnglish (US)
Pages (from-to)435-449
Number of pages15
JournalSIAM Journal on Matrix Analysis and Applications
Volume18
Issue number2
DOIs
StatePublished - Apr 1997

Keywords

  • Block-GMRES
  • Deflated iterations
  • Krylov methods

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