slaed6.f File Reference

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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.

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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.

Download SLAED6 + dependencies [TGZ] [ZIP] [TXT]

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:

[in]	KNITER	KNITER is INTEGER Refer to SLAED4 for its significance.
[in]	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.
[in]	RHO	RHO is REAL Refer to the equation f(x) above.
[in]	D	D is REAL array, dimension (3) D satisfies d(1) < d(2) < d(3).
[in]	Z	Z is REAL array, dimension (3) Each of the elements in z must be positive.
[in]	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).
[out]	TAU	TAU is REAL The root of the equation f(x).
[out]	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.

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