A black-box rational Arnoldi variant for Cauchy-Stieltjes matrix functions

Güttel, Stefan and Knizhnerman, Leonid (2012) A black-box rational Arnoldi variant for Cauchy-Stieltjes matrix functions. [MIMS Preprint]

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Rational Arnoldi is a powerful method for approximating functions of large sparse matrices times a vector. The selection of asymptotically optimal parameters for this method is crucial for its fast convergence. We present and investigate a novel strategy for the automated parameter selection when the function to be approximated is of Cauchy-Stieltjes (or Markov) type, such as the matrix square root or the logarithm. The performance of this approach is demonstrated by numerical examples involving symmetric and nonsymmetric matrices. These examples suggest that our black-box method performs at least as well, and typically better, as the standard rational Arnoldi method with parameters being manually optimized for a given matrix.

Item Type: MIMS Preprint
Uncontrolled Keywords: rational Arnoldi method, matrix square root, matrix logarithm, optimal parameters
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Stefan Güttel
Date Deposited: 16 Oct 2012
Last Modified: 08 Nov 2017 18:18
URI: https://eprints.maths.manchester.ac.uk/id/eprint/1883

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