Inexact low-rank Newton-ADI method for large-scale algebraic Riccati equations / Peter Benner, Matthias Heinkenschloss, Jens Saak, Heiko K. Weichelt

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.