---
name: "slaed6"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/slaed6/3lapack"
---

# slaed6(3lapack)

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

## NAME

SLAED6 - computes the positive or negative root (closest to the origin) of  [z(1)](/z/1.md) 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/1.md)        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.