# dlaed6.f man page

dlaed6.f —

## Synopsis

### Functions/Subroutines

subroutinedlaed6(KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO)DLAED6used by sstedc. Computes one Newton step in solution of the secular equation.

## Function/Subroutine Documentation

### subroutine dlaed6 (integerKNITER, logicalORGATI, double precisionRHO, double precision, dimension( 3 )D, double precision, dimension( 3 )Z, double precisionFINIT, double precisionTAU, integerINFO)

**DLAED6** used by sstedc. Computes one Newton step in solution of the secular equation.

**Purpose:**

```
DLAED6 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 DLAED4 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 DLAED4 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
DLAED4 for further details.
```

*RHO*

```
RHO is DOUBLE PRECISION
Refer to the equation f(x) above.
```

*D*

```
D is DOUBLE PRECISION array, dimension (3)
D satisfies d(1) < d(2) < d(3).
```

*Z*

```
Z is DOUBLE PRECISION array, dimension (3)
Each of the elements in z must be positive.
```

*FINIT*

```
FINIT is DOUBLE PRECISION
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 DOUBLE PRECISION
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 dlaed6.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

dlaed6(3) is an alias of dlaed6.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK