Preconditioning for nonsymmetry and time-dependence

Eleanor McDonald, Sean Hon, Jennifer Pestana, Andrew Wathen

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In this short paper, we decribe at least one simple and frequently arising situation |that of nonsymmetric real Toeplitz (constant diagonal) matrices| where we can guarantee rapid convergence of the appropriate iterative method by manipulating the problem into a symmetric form without recourse to the normal equations. This trick can be applied regardless of the nonnormality of the Toeplitz matrix. We also propose a symmetric and positive definite preconditioner for this situation which is proved to cluster eigenvalues and is by consequence guaranteed to ensure convergence in a number of iterations independent of the matrix dimension.
Original languageEnglish
Number of pages11
Publication statusPublished - 14 Apr 2016
Event23rd International Conference on Domain Decomposition Methods - Jeju Island, Korea, Democratic People's Republic of
Duration: 6 Jul 201510 Jul 2015


Conference23rd International Conference on Domain Decomposition Methods
Abbreviated titleDD 23
Country/TerritoryKorea, Democratic People's Republic of
CityJeju Island


  • preconditioning
  • nonsymmetric real Toeplitz matrices
  • Toeplitz matrix
  • time-dependence


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