.TH "laed6" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
laed6 \- laed6: D&C step: secular equation Newton step
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBdlaed6\fP (kniter, orgati, rho, d, z, finit, tau, info)"
.br
.RI "\fBDLAED6\fP used by DSTEDC\&. Computes one Newton step in solution of the secular equation\&. "
.ti -1c
.RI "subroutine \fBslaed6\fP (kniter, orgati, rho, d, z, finit, tau, info)"
.br
.RI "\fBSLAED6\fP used by SSTEDC\&. Computes one Newton step in solution of the secular equation\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine dlaed6 (integer kniter, logical orgati, double precision rho, double precision, dimension( 3 ) d, double precision, dimension( 3 ) z, double precision finit, double precision tau, integer info)"

.PP
\fBDLAED6\fP used by DSTEDC\&. Computes one Newton step in solution of the secular equation\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIKNITER\fP 
.PP
.nf
          KNITER is INTEGER
               Refer to DLAED4 for its significance\&.
.fi
.PP
.br
\fIORGATI\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIRHO\fP 
.PP
.nf
          RHO is DOUBLE PRECISION
               Refer to the equation f(x) above\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (3)
               D satisfies d(1) < d(2) < d(3)\&.
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
          Z is DOUBLE PRECISION array, dimension (3)
               Each of the elements in z must be positive\&.
.fi
.PP
.br
\fIFINIT\fP 
.PP
.nf
          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)\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is DOUBLE PRECISION
               The root of the equation f(x)\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
               = 0: successful exit
               > 0: if INFO = 1, failure to converge
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  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\&.
.fi
.PP
 
.RE
.PP
\fBContributors:\fP
.RS 4
Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA 
.RE
.PP

.SS "subroutine slaed6 (integer kniter, logical orgati, real rho, real, dimension( 3 ) d, real, dimension( 3 ) z, real finit, real tau, integer info)"

.PP
\fBSLAED6\fP used by SSTEDC\&. Computes one Newton step in solution of the secular equation\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIKNITER\fP 
.PP
.nf
          KNITER is INTEGER
               Refer to SLAED4 for its significance\&.
.fi
.PP
.br
\fIORGATI\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIRHO\fP 
.PP
.nf
          RHO is REAL
               Refer to the equation f(x) above\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is REAL array, dimension (3)
               D satisfies d(1) < d(2) < d(3)\&.
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
          Z is REAL array, dimension (3)
               Each of the elements in z must be positive\&.
.fi
.PP
.br
\fIFINIT\fP 
.PP
.nf
          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)\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is REAL
               The root of the equation f(x)\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
               = 0: successful exit
               > 0: if INFO = 1, failure to converge
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  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\&.
.fi
.PP
 
.RE
.PP
\fBContributors:\fP
.RS 4
Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA 
.RE
.PP

.SH "Author"
.PP 
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