SB04RY

Solving a system of equations in Hessenberg form with one right-hand side

Purpose

  To solve a system of equations in Hessenberg form with one
  right-hand side.

      SUBROUTINE SB04RY( RC, UL, M, A, LDA, LAMBDA, D, TOL, IWORK,
     $                   DWORK, LDDWOR, INFO )
C     .. Scalar Arguments ..
      CHARACTER         RC, UL
      INTEGER           INFO, LDA, LDDWOR, M
      DOUBLE PRECISION  LAMBDA, TOL
C     .. Array Arguments ..
      INTEGER           IWORK(*)
      DOUBLE PRECISION  A(LDA,*), D(*), DWORK(LDDWOR,*)

Mode Parameters

  RC      CHARACTER*1
          Indicates processing by columns or rows, as follows:
          = 'R':  Row transformations are applied;
          = 'C':  Column transformations are applied.

  UL      CHARACTER*1
          Indicates whether A is upper or lower Hessenberg matrix,
          as follows:
          = 'U':  A is upper Hessenberg;
          = 'L':  A is lower Hessenberg.

  M       (input) INTEGER
          The order of the matrix A.  M >= 0.

  A       (input) DOUBLE PRECISION array, dimension (LDA,M)
          The leading M-by-M part of this array must contain a
          matrix A in Hessenberg form.

  LDA     INTEGER
          The leading dimension of array A.  LDA >= MAX(1,M).

  LAMBDA  (input) DOUBLE PRECISION
          This variable must contain the value to be multiplied with
          the elements of A.

  D       (input/output) DOUBLE PRECISION array, dimension (M)
          On entry, this array must contain the right-hand side
          vector of the Hessenberg system.
          On exit, if INFO = 0, this array contains the solution
          vector of the Hessenberg system.

  TOL     DOUBLE PRECISION
          The tolerance to be used to test for near singularity of
          the triangular factor R of the Hessenberg matrix. A matrix
          whose estimated condition number is less than 1/TOL is
          considered to be nonsingular.

  IWORK   INTEGER array, dimension (M)

  DWORK   DOUBLE PRECISION array, dimension (LDDWOR,M+3)
          The leading M-by-M part of this array is used for
          computing the triangular factor of the QR decomposition
          of the Hessenberg matrix. The remaining 3*M elements are
          used as workspace for the computation of the reciprocal
          condition estimate.

  LDDWOR  INTEGER
          The leading dimension of array DWORK.  LDDWOR >= MAX(1,M).

  INFO    INTEGER
          = 0:  successful exit;
          = 1:  if the Hessenberg matrix is (numerically) singular.
                That is, its estimated reciprocal condition number
                is less than or equal to TOL.

  None.

  None

Program Text

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