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

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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.

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Authors and Affiliations

  1. Max-Planck-Institute for Mathematics in the Sciences Inselstr. 22–26 D-04103 Leipzig Germany e-mails: {lgr,wh,bokh}@mis.mpg.de, , , , , , DE

    L. Grasedyck, W. Hackbusch & B. N. Khoromskij

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  1. L. Grasedyck
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  2. W. Hackbusch
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  3. B. N. Khoromskij
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Received July 30, 2002; revised December 16, 2002 Published online: April 22, 2003

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Grasedyck, L., Hackbusch, W. & Khoromskij, B. Solution of Large Scale Algebraic Matrix Riccati Equations by Use of Hierarchical Matrices. Computing 70, 121–165 (2003). https://doi.org/10.1007/s00607-002-1470-0

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  • DOI: https://doi.org/10.1007/s00607-002-1470-0

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