1SLAED6(1)               LAPACK routine (version 3.1.1)               SLAED6(1)
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NAME

6       SLAED6 - the positive or negative root (closest to the origin) of  z(1)
7       z(2) z(3) f(x) = rho +  ---------  +  ----------  +  ---------   d(1)-x
8       d(2)-x d(3)-x  It is assumed that   if ORGATI = .true
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SYNOPSIS

11       SUBROUTINE SLAED6( KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO )
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13           LOGICAL        ORGATI
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15           INTEGER        INFO, KNITER
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17           REAL           FINIT, RHO, TAU
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19           REAL           D( 3 ), Z( 3 )
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PURPOSE

22       SLAED6  computes  the positive or negative root (closest to the origin)
23       of
24                        z(1)        z(2)        z(3) f(x) =   rho +  ---------
25       + ---------- + ---------
26                       d(1)-x      d(2)-x      d(3)-x
27             otherwise it is between d(1) and d(2)
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29       This  routine  will  be called by SLAED4 when necessary. In most cases,
30       the root sought is the smallest in magnitude, though it might not be in
31       some extremely rare situations.
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ARGUMENTS

35       KNITER       (input) INTEGER
36                    Refer to SLAED4 for its significance.
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38       ORGATI       (input) LOGICAL
39                    If  ORGATI  is  true,  the needed root is between d(2) and
40                    d(3); otherwise it is between d(1) and d(2).   See  SLAED4
41                    for further details.
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43       RHO          (input) REAL
44                    Refer to the equation f(x) above.
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46       D            (input) REAL array, dimension (3)
47                    D satisfies d(1) < d(2) < d(3).
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49       Z            (input) REAL array, dimension (3)
50                    Each of the elements in z must be positive.
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52       FINIT        (input) REAL
53                    The  value  of  f  at  0. It is more accurate than the one
54                    evaluated inside this routine (if someone wants to do so).
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56       TAU          (output) REAL
57                    The root of the equation f(x).
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59       INFO         (output) INTEGER
60                    = 0: successful exit
61                    > 0: if INFO = 1, failure to converge
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FURTHER DETAILS

64       30/06/99: Based on contributions by
65          Ren-Cang Li, Computer Science Division, University of California
66          at Berkeley, USA
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68       10/02/03: This version has a few statements commented  out  for  thread
69       safety
70          (machine parameters are computed on each entry). SJH.
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72       05/10/06: Modified from a new version of Ren-Cang Li, use
73          Gragg-Thornton-Warner cubic convergent scheme for better stability.
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78 LAPACK routine (version 3.1.1)  February 2007                       SLAED6(1)
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