slaed6.f(3)							      LAPACK							       slaed6.f(3)

NAME

       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 (integerKNITER, logicalORGATI, realRHO, real, dimension( 3 )D, real, dimension( 3 )Z, realFINIT, realTAU, integerINFO)
       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:
	   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 slaed6.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       slaed6.f(3)