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Functions of rational Krylov space matrices and their decay properties
Type of publication: Article
Citation:
Publication status: Published
Journal: Numerische Mathematik
Volume: 148
Year: 2021
Month: September
Pages: 99–126
DOI: https://doi.org/10.1007/s00211-021-01198-4
Abstract: Rational Krylov subspaces have become a fundamental ingredient in numerical linear algebra methods associated with reduction strategies. Nonetheless, many structural properties of the reduced matrices in these subspaces are not fully understood. We advance in this analysis by deriving bounds on the entries of rational Krylov reduced matrices and of their functions, that ensure an a-priori decay of their entries as we move away from the main diagonal. As opposed to other decay pattern results in the literature, these properties hold in spite of the lack of any banded structure in the considered matrices. Numerical experiments illustrate the quality of our results.
Keywords:
Authors Pozza, Stefano
Simoncini, Valeria
Added by: [SP]
Total mark: 0
Attachments
  • PozSim2020.pdf
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