## MB03HZ

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

[Specification] [Arguments] [Method] [References] [Comments] [Example]

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.

Specification

          SUBROUTINE MB03HZ( S11, S12, H11, H12, CO, SI )
    C     .. Scalar Arguments ..
          DOUBLE PRECISION   CO
          COMPLEX*16         H11, H12, S11, S12, SI

Arguments

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.

Method

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

References

      [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.

Numerical Aspects

      The algorithm is numerically backward stable.

Further Comments

      None

Example

Program Text

      None

Program Data

      None

Program Results

      None

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