publication . Article . Journal . Other literature type . 2019

Approximate residual minimizing shift parameters for the low-rank ADI iteration

Patrick Kürschner;
Open Access
  • Published: 09 Sep 2019
  • Publisher: Kent State University Library
Abstract
The low-rank alternating directions implicit (LR-ADI) iteration is a frequently employed method for efficiently computing low-rank approximate solutions of large-scale Lyapunov equations. In order to achieve a rapid error reduction, the iteration requires shift parameters whose selection and generation is often a difficult task, especially for nonsymmetric matrices in the Lyapunov equation. This article represents a follow up of Benner et al. [Electron. Trans. Numer. Anal., 43 (2014–2015), pp. 142–162] and investigates self-generating shift parameters based on a minimization principle for the Lyapunov residual norm. Since the involved objective functions are too...
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free text keywords: Lyapunov equation, alternating directions implicit, low-rank approximation, shift parameters,Mathematics, Physics and Space Research, Analysis, Residual, Applied mathematics, Mathematics
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