MB03HZ

Exchanging eigenvalues of a complex 2-by-2 skew-Hamiltonian/Hamiltonian pencil in structured Schur form

Purpose

  To compute a unitary matrix Q for a complex regular 2-by-2 
  skew-Hamiltonian/Hamiltonian pencil aS - bH with

      (  S11  S12  )        (  H11  H12  )
  S = (            ),   H = (            ),
      (   0   S11' )        (   0  -H11' )

  such that J Q' J' (aS - bH) Q is upper triangular but the
  eigenvalues are in reversed order. The matrix Q is represented by

      (  CO  SI  )
  Q = (          ).
      ( -SI' CO  )

  The notation M' denotes the conjugate transpose of the matrix M.

Input/Output Parameters

  S11     (input) COMPLEX*16
          Upper left element of the skew-Hamiltonian matrix S.

  S12     (input) COMPLEX*16
          Upper right element of the skew-Hamiltonian matrix S.

  H11     (input) COMPLEX*16
          Upper left element of the Hamiltonian matrix H.

  H12     (input) COMPLEX*16
          Upper right element of the Hamiltonian matrix H.

  CO      (output) DOUBLE PRECISION
          Upper left element of Q.

  SI      (output) COMPLEX*16
          Upper right element of Q.

  The algorithm uses unitary transformations as described on page 43
  in [1].

  [1] Benner, P., Byers, R., Mehrmann, V. and Xu, H.
      Numerical Computation of Deflating Subspaces of Embedded
      Hamiltonian Pencils.
      Tech. Rep. SFB393/99-15, Technical University Chemnitz,
      Germany, June 1999.

  The algorithm is numerically backward stable.

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Program Text

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