subroutine slaed6 (KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO)
SLAED6 used by sstedc. Computes one Newton step in solution of the secular equation.
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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
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:
Definition at line 142 of file slaed6.f.
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