---
name: "slaed6"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/slaed6.f"
---

# slaed6(3)

Part of [slaed6.f(3)](/slaed6.f/3.md).

## NAME

SRC/slaed6.f

## SYNOPSIS

### 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**

*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.

**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 **139** of file **slaed6.f**.

## Author

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