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## slaed6()

subroutine slaed6 | ( | integer | kniter,
|  | logical | orgati,
|  | real | rho,
|  | real, dimension( 3 ) | d,
|  | real, dimension( 3 ) | z,
|  | real | finit,
|  | real | tau,
|  | integer | info )

SLAED6 used by SSTEDC. Computes one Newton step in solution of the secular equation.

Download SLAED6 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> SLAED6 computes the positive or negative root (closest to the origin)
      !> of
      !>                  z(1)        z(2)        z(3)
      !> f(x) =   rho + --------- + ---------- + ---------
      !>                 d(1)-x      d(2)-x      d(3)-x
      !>
      !> It is assumed that
      !>
      !>       if ORGATI = .true. the root is between d(2) and d(3);
      !>       otherwise it is between d(1) and d(2)
      !>
      !> This routine will be called by SLAED4 when necessary. In most cases,
      !> the root sought is the smallest in magnitude, though it might not be
      !> in some extremely rare situations.
      !>

Parameters

  [in]

  KNITER

      !>          KNITER is INTEGER
      !>               Refer to SLAED4 for its significance.
      !>

  [in]

  ORGATI

      !>          ORGATI is LOGICAL
      !>               If ORGATI is true, the needed root is between d(2) and
      !>               d(3); otherwise it is between d(1) and d(2).  See
      !>               SLAED4 for further details.
      !>

  [in]

  RHO

      !>          RHO is REAL
      !>               Refer to the equation f(x) above.
      !>

  [in]

  D

      !>          D is REAL array, dimension (3)
      !>               D satisfies d(1) < d(2) < d(3).
      !>

  [in]

  Z

      !>          Z is REAL array, dimension (3)
      !>               Each of the elements in z must be positive.
      !>

  [in]

  FINIT

      !>          FINIT is REAL
      !>               The value of f at 0. It is more accurate than the one
      !>               evaluated inside this routine (if someone wants to do
      !>               so).
      !>

  [out]

  TAU

      !>          TAU is REAL
      !>               The root of the equation f(x).
      !>

  [out]

  INFO

      !>          INFO is INTEGER
      !>               = 0: successful exit
      !>               > 0: if INFO = 1, failure to converge
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.

Further Details:

      !>
      !>  10/02/03: This version has a few statements commented out for thread
      !>  safety (machine parameters are computed on each entry). SJH.
      !>
      !>  05/10/06: Modified from a new version of Ren-Cang Li, use
      !>     Gragg-Thornton-Warner cubic convergent scheme for better stability.
      !>

Contributors:
  Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA