# slaed6.f man page

slaed6.f —

## Synopsis

### Functions/Subroutines

subroutineslaed6(KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO)SLAED6used by sstedc. Computes one Newton step in solution of the secular equation.

## Function/Subroutine Documentation

### subroutine slaed6 (integerKNITER, logicalORGATI, realRHO, real, dimension( 3 )D, real, dimension( 3 )Z, realFINIT, realTAU, integerINFO)

**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:**

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.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

slaed6(3) is an alias of slaed6.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK