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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