SRC/dlaed6.f(3)

NAME
SRC/dlaed6.f

SYNOPSIS

  Functions/Subroutines
subroutine dlaed6 (kniter, orgati, rho, d, z, finit, tau, info)
DLAED6 used by DSTEDC. Computes one Newton step in solution of the secular equation.

Function/Subroutine Documentation

  subroutine dlaed6 (integer kniter, logical orgati, double precision rho, double precision, dimension( 3 ) d, double precision, dimension( 3 ) z, double precision finit, double precision tau, integer info)

DLAED6 used by DSTEDC. Computes one Newton step in solution of the secular equation.

Purpose:

     DLAED6 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 DLAED4 when necessary. In most cases,
     the root sought is the smallest in magnitude, though it might not be
     in some extremely rare situations.

Parameters
    KNITER

              KNITER is INTEGER
                   Refer to DLAED4 for its significance.

    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
                   DLAED4 for further details.

    RHO

              RHO is DOUBLE PRECISION
                   Refer to the equation f(x) above.

    D

              D is DOUBLE PRECISION array, dimension (3)
                   D satisfies d(1) < d(2) < d(3).

    Z

              Z is DOUBLE PRECISION array, dimension (3)
                   Each of the elements in z must be positive.

    FINIT

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

    TAU

              TAU is DOUBLE PRECISION
                   The root of the equation f(x).

    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

Definition at line 139 of file dlaed6.f.

Author

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