The Mathematical Institute, University of Oxford, Eprints Archive

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

Guettel, Stefan and Knizhnerman, Leonid (2012) A black-box rational Arnoldi variant for Cauchy-Stieltjes matrix functions. Technical Report. SIAM. (Submitted)

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Abstract

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:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1466
Deposited By:Lotti Ekert
Deposited On:21 Feb 2012 07:36
Last Modified:21 Feb 2012 07:36

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