slaed6.f(3)

NAME
slaed6.f

SYNOPSIS

  Functions/Subroutines
subroutine slaed6 (KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO)
SLAED6 used by sstedc. Computes one Newton step in solution of the secular equation.

Function/Subroutine Documentation

  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.

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:
    KNITER

              KNITER is INTEGER
                   Refer to SLAED4 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
                   SLAED4 for further details.

    RHO

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

    D

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

    Z

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

    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).

    TAU

              TAU is REAL
                   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.

Date:
    December 2016

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 142 of file slaed6.f.

Author

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