Computing

, Volume 70, Issue 2, pp 121–165 | Cite as

Solution of Large Scale Algebraic Matrix Riccati Equations by Use of Hierarchical Matrices

  • L. Grasedyck
  • W. Hackbusch
  • B. N. Khoromskij

In previous papers, a class of hierarchical matrices (ℋ-matrices) is introduced which are data-sparse and allow an approximate matrix arithmetic of almost optimal complexity. Here, we investigate a new approach to exploit the ℋ-matrix structure for the solution of large scale Lyapunov and Riccati equations as they typically arise for optimal control problems where the constraint is a partial differential equation of elliptic type. This approach leads to an algorithm of linear-logarithmic complexity in the size of the matrices.

AMS Subject Classifications: 65F05, 65F30, 65F50. 
Keywords: Hierarchical matrices, data-sparse approximations, formatted matrix operations, fast solvers, Lyapunov equations, Riccati equations, control problems. 

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Copyright information

© Springer-Verlag Wien 2003

Authors and Affiliations

  • L. Grasedyck
    • 1
  • W. Hackbusch
    • 1
  • B. N. Khoromskij
    • 1
  1. 1.Max-Planck-Institute for Mathematics in the Sciences Inselstr. 22–26 D-04103 Leipzig Germany e-mails: {lgr,wh,bokh}@mis.mpg.deDE

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