Preprint No. MPIMD/15-06

Title: Inexact low-rank Newton-ADI method for large-scale algebraic Riccati equations

Author(s): Peter Benner, Matthias Heinkenschloss, Jens Saak, Heiko K. Weichelt


Date: 2015-05-05

Revised: 2015-09-14


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


author = {Peter Benner and Matthias Heinkenschloss and Jens Saak and Heiko K. Weichelt},
title = {Inexact low-rank Newton-ADI method for large-scale algebraic Riccati equations},
number = {MPIMD/15-06},
month = may,
year = 2015,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{}},

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