# ?laed6

Used by sstedc/dstedc. Computes one Newton step in solution of the secular equation.

## Syntax

call slaed6( kniter, orgati, rho, d, z, finit, tau, info )

call dlaed6( kniter, orgati, rho, d, z, finit, tau, info )

## Description

This routine computes the positive or negative root (closest to the origin) of

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 is called by ?laed4 when necessary. In most cases, the root sought is the smallest in magnitude, though it might not be in some extremely rare situations.

## Input Parameters

kniter

  INTEGER.

  Refer to ?laed4 for its significance.

orgati

  LOGICAL.

  If `orgati = .TRUE.`, the needed root is between d(2) and d(3); otherwise it is between d(1) and d(2). See ?laed4 for further details.

rho

  REAL for slaed6

  DOUBLE PRECISION for dlaed6

  Refer to the equation for f(x) above.

d, z

  REAL for slaed6

  DOUBLE PRECISION for dlaed6

  Arrays, dimension (3) each.

  The array d satisfies `d(1) < d(2) < d(3)`.

  Each of the elements in the array z must be positive.

finit

  REAL for slaed6

  DOUBLE PRECISION for dlaed6

  The value of f(x) at 0. It is more accurate than the one evaluated inside this routine (if someone wants to do so).

## Output Parameters

tau

  REAL for slaed6

  DOUBLE PRECISION for dlaed6

  The root of the equation for f(x).

info

  INTEGER.

  If `info = 0`, the execution is successful.

  If `info = 1`, failure to converge.

Parent topic: Auxiliary Routines