MB02TD

Estimation of the reciprocal condition number of an upper Hessenberg matrix

Purpose

  To estimate the reciprocal of the condition number of an upper
  Hessenberg matrix H, in either the 1-norm or the infinity-norm,
  using the LU factorization computed by MB02SD.

      SUBROUTINE MB02TD( NORM, N, HNORM, H, LDH, IPIV, RCOND, IWORK,
     $                   DWORK, INFO )
C     .. Scalar Arguments ..
      CHARACTER          NORM
      INTEGER            INFO, LDH, N
      DOUBLE PRECISION   HNORM, RCOND
C     .. Array Arguments ..
      INTEGER            IPIV( * ), IWORK( * )
      DOUBLE PRECISION   DWORK( * ), H( LDH, * )

Mode Parameters

  NORM    CHARACTER*1
          Specifies whether the 1-norm condition number or the
          infinity-norm condition number is required:
          = '1' or 'O':  1-norm;
          = 'I':         Infinity-norm.

  N       (input) INTEGER
          The order of the matrix H.  N >= 0.

  HNORM   (input) DOUBLE PRECISION
          If NORM = '1' or 'O', the 1-norm of the original matrix H.
          If NORM = 'I', the infinity-norm of the original matrix H.

  H       (input) DOUBLE PRECISION array, dimension (LDH,N)
          The factors L and U from the factorization H = P*L*U
          as computed by MB02SD.

  LDH     INTEGER
          The leading dimension of the array H.  LDH >= max(1,N).

  IPIV    (input) INTEGER array, dimension (N)
          The pivot indices; for 1 <= i <= N, row i of the matrix
          was interchanged with row IPIV(i).

  RCOND   (output) DOUBLE PRECISION
          The reciprocal of the condition number of the matrix H,
          computed as RCOND = 1/(norm(H) * norm(inv(H))).

  IWORK   INTEGER array, dimension (N)

  DWORK   DOUBLE PRECISION array, dimension (3*N)

  INFO    INTEGER
          = 0:  successful exit;
          < 0:  if INFO = -i, the i-th argument had an illegal
                value.

  An estimate is obtained for norm(inv(H)), and the reciprocal of
  the condition number is computed as
     RCOND = 1 / ( norm(H) * norm(inv(H)) ).

  -

                             2
  The algorithm requires 0( N ) operations.

  None

Program Text

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