LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
slaed6.f File Reference

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## 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:
 [in] KNITER ``` KNITER is INTEGER Refer to SLAED4 for its significance.``` [in] 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.``` [in] RHO ``` RHO is REAL Refer to the equation f(x) above.``` [in] D ``` D is REAL array, dimension (3) D satisfies d(1) < d(2) < d(3).``` [in] Z ``` Z is REAL array, dimension (3) Each of the elements in z must be positive.``` [in] 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).``` [out] TAU ``` TAU is REAL The root of the equation f(x).``` [out] INFO ``` INFO is INTEGER = 0: successful exit > 0: if INFO = 1, failure to converge```
Date:
September 2012
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 141 of file slaed6.f.

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