Abstract
Riccati and Lyapunov equations can be solved using the recursive matrix sign method applied to symmetric matrices constructed from the corresponding Hamiltonian matrices. In this paper we derive an efficient systolic implementation of that algorithm where theLDL T andUDU T decompositions of those symmetric matrices are propagated. As a result the solution of a class of Riccati and Lyapunov equations can be obtained inO(n) time steps on a bidimensional (triangular) grid ofO(n 2) processors, leading to an optimal speedup.
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Charlier, J.P., Van Dooren, P. A systolic algorithm for riccati and lyapunov equations. Math. Control Signal Systems 2, 109–136 (1989). https://doi.org/10.1007/BF02551818
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DOI: https://doi.org/10.1007/BF02551818