Further Analysis of Minimum Residual Iterations

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The convergence behaviour of a number of algorithms based on minimizing residual norms over Krylov subspaces is not well understood. Residual or error bounds currently available are either too loose or depend on unknown constants that can be very large. In this paper we take another look at traditional as well as alternative ways of obtaining upper bounds on residual norms. In particular, we derive inequalities that utilize Chebyshev polynomials and compare them with standard inequalities.

Original languageEnglish (US)
Pages (from-to)67-93
Number of pages27
JournalNumerical Linear Algebra with Applications
Issue number2
StatePublished - Jan 1 2000


  • Krylov subspace techniques
  • Minimal residual methods


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