Inexact low-rank Newton-ADI method for large-scale algebraic Riccati equations / Peter Benner, Matthias Heinkenschloss, Jens Saak, Heiko K. Weichelt
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Inexact low-rank Newton-ADI method for large-scale algebraic Riccati equations
Discovery
870916386
URN
urn:nbn:de:gbv:3:2-64725
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Publication history
Magdeburg : Max Planck Institute for Dynamics of Complex Technical Systems, September 9, 2015
Content
1 Online-Ressource (28 Seiten = 0,45 MB)
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Language
eng
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Abstract
Abstract: This paper improves the inexact Kleinman-Newton method by incorporating a line search and by systematically integrating the low-rank structure resulting from ADI methods for the approximate solution of the Lyapunov equation that needs to be solved to compute the Kleinman-Newton step. A convergence result is presented that tailors the convergence proof for general inexact Newton methods to the structure of Riccati equations and avoids positive semi-deniteness ssumptions on the Lyapunov equation residual, which in general do not hold for ow-rank approaches. On a test example, the improved inexact Kleinman-Newton ethod is seven to twelve times faster than the exact Kleinman-Newton method ithout line search; the addition of the line search to the inexact Kleinman-Newton method alone can reduce computation time by up to a factor of two.
Series
Max Planck Institute Magdeburg Preprints ; 15-06 ppn:870173030