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dlaed6.f(3) LAPACK dlaed6.f(3)

NAME

dlaed6.f -

SYNOPSIS

Functions/Subroutines


subroutine dlaed6 (KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO)
DLAED6 used by sstedc. Computes one Newton step in solution of the secular equation.

Function/Subroutine Documentation

subroutine dlaed6 (integerKNITER, logicalORGATI, double precisionRHO, double precision, dimension( 3 )D, double precision, dimension( 3 )Z, double precisionFINIT, double precisionTAU, integerINFO)

DLAED6 used by sstedc. Computes one Newton step in solution of the secular equation.

Purpose:


DLAED6 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 DLAED4 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 DLAED4 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
DLAED4 for further details.

RHO


RHO is DOUBLE PRECISION
Refer to the equation f(x) above.

D


D is DOUBLE PRECISION array, dimension (3)
D satisfies d(1) < d(2) < d(3).

Z


Z is DOUBLE PRECISION array, dimension (3)
Each of the elements in z must be positive.

FINIT


FINIT is DOUBLE PRECISION
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 DOUBLE PRECISION
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 dlaed6.f.

Author

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Tue Sep 25 2012 Version 3.4.2