The Mathematical Institute, University of Oxford, Eprints Archive

Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection

Guettel, Stefan (2012) Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection. Technical Report. Wiley. (Submitted)

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Abstract

Matrix functions are a central topic of linear algebra, and problems of their numerical approximation appear increasingly often in scientific computing. We review various rational Krylov methods for the computation of large-scale matrix functions. Emphasis is put on the rational Arnoldi method and variants thereof, namely, the extended Krylov subspace method and the shift-and-invert Arnoldi method, but we also discuss the nonorthogonal generalized Leja point (or PAIN) method. The issue of optimal pole selection for rational Krylov methods applied for approximating the resolvent and exponential function, and functions of Markov type, is treated in some detail.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1502
Deposited By:Lotti Ekert
Deposited On:29 Mar 2012 07:54
Last Modified:29 Mar 2012 07:54

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