## Hamiltonian and Symplectic Algorithms for the Algebraic Riccati Equation |

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### Contents

Chapter page | 1 |

SYMPLECTIC ANO HAMILTONIAN MATRICES | 13 |

CONOITION | 38 |

Copyright | |

7 other sections not shown

### Common terms and phrases

algebraic Riccati equation approximately arithmetic ARRAY OF DIMENSION ARRAY OF LENGTH calculated CALL V3REF CEOM columns components CONTINUE convergence diagonal DIMENSION AT LEAST DOUBLE PRECISION DP ARRAY EFREV eigenvalues EISPACK ENDIF flops HAM(A Hamiltonian matrix Hamiltonian QR step Hamiltonian-Hessenberg form Hamiltonian-Schur decomposition Hessenberg form Householder reflection IERR IFLAG INCU INPUT INTEGER SCALAR invariant subspace ITERAT ITMAX ITOP JSUBU LALC LEAST MDECN LENGTH AT LEAST LJSUBG LLCA lower Hessenberg Lyapunov equation MDEC MOEC MSUBU N:(INPUT Newton's method numerically stable OERZ OOUBLE orthogonal matrix orthogonal similarity transformations OUTPUT OVERWRITTEN perturbation problem QR algorithm QR factorization QR iteration replaced Rnxn rotations rounding errors rows Schur decomposition Section sign function sign function method solve square reduced stabilizing solution SUBROUTINE SYMMETRIC MATRIX symplectic matrices symplectic QR Theorem upper Hessenberg upper triangular vector X X X XXX XXX XXX xxxxx zero structure