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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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