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.