SLAED6(1) LAPACK routine (version 3.2) SLAED6(1)NAME
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
SYNOPSIS
SUBROUTINE SLAED6( KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO )
LOGICAL ORGATI
INTEGER INFO, KNITER
REAL FINIT, RHO, TAU
REAL D( 3 ), Z( 3 )
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
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.
ARGUMENTS
KNITER (input) INTEGER
Refer to SLAED4 for its significance.
ORGATI (input) 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 (input) REAL
Refer to the equation f(x) above.
D (input) REAL array, dimension (3)
D satisfies d(1) < d(2) < d(3).
Z (input) REAL array, dimension (3)
Each of the elements in z must be positive.
FINIT (input) 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 (output) REAL
The root of the equation f(x).
INFO (output) INTEGER
= 0: successful exit
> 0: if INFO = 1, failure to converge
FURTHER DETAILS
30/06/99: Based on contributions by
Ren-Cang Li, Computer Science Division, University of California
at Berkeley, USA
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.
LAPACK routine (version 3.2) November 2008 SLAED6(1)
