# slaed6.f man page

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.

**Date:**December 2016

**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 142 of file slaed6.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page slaed6(3) is an alias of slaed6.f(3).

Sat Jun 24 2017 Version 3.7.1 LAPACK