.TH "SRC/dlarrk.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/dlarrk.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBdlarrk\fP (n, iw, gl, gu, d, e2, pivmin, reltol, w, werr, info)"
.br
.RI "\fBDLARRK\fP computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dlarrk (integer n, integer iw, double precision gl, double precision gu, double precision, dimension( * ) d, double precision, dimension( * ) e2, double precision pivmin, double precision reltol, double precision w, double precision werr, integer info)"

.PP
\fBDLARRK\fP computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DLARRK computes one eigenvalue of a symmetric tridiagonal
 matrix T to suitable accuracy\&. This is an auxiliary code to be
 called from DSTEMR\&.

 To avoid overflow, the matrix must be scaled so that its
 largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest
 accuracy, it should not be much smaller than that\&.

 See W\&. Kahan 'Accurate Eigenvalues of a Symmetric Tridiagonal
 Matrix', Report CS41, Computer Science Dept\&., Stanford
 University, July 21, 1966\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the tridiagonal matrix T\&.  N >= 0\&.
.fi
.PP
.br
\fIIW\fP 
.PP
.nf
          IW is INTEGER
          The index of the eigenvalues to be returned\&.
.fi
.PP
.br
\fIGL\fP 
.PP
.nf
          GL is DOUBLE PRECISION
.fi
.PP
.br
\fIGU\fP 
.PP
.nf
          GU is DOUBLE PRECISION
          An upper and a lower bound on the eigenvalue\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the tridiagonal matrix T\&.
.fi
.PP
.br
\fIE2\fP 
.PP
.nf
          E2 is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) squared off-diagonal elements of the tridiagonal matrix T\&.
.fi
.PP
.br
\fIPIVMIN\fP 
.PP
.nf
          PIVMIN is DOUBLE PRECISION
          The minimum pivot allowed in the Sturm sequence for T\&.
.fi
.PP
.br
\fIRELTOL\fP 
.PP
.nf
          RELTOL is DOUBLE PRECISION
          The minimum relative width of an interval\&.  When an interval
          is narrower than RELTOL times the larger (in
          magnitude) endpoint, then it is considered to be
          sufficiently small, i\&.e\&., converged\&.  Note: this should
          always be at least radix*machine epsilon\&.
.fi
.PP
.br
\fIW\fP 
.PP
.nf
          W is DOUBLE PRECISION
.fi
.PP
.br
\fIWERR\fP 
.PP
.nf
          WERR is DOUBLE PRECISION
          The error bound on the corresponding eigenvalue approximation
          in W\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:       Eigenvalue converged
          = -1:      Eigenvalue did NOT converge
.fi
.PP
 
.RE
.PP
\fBInternal Parameters:\fP
.RS 4

.PP
.nf
  FUDGE   DOUBLE PRECISION, default = 2
          A 'fudge factor' to widen the Gershgorin intervals\&.
.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

.PP
Definition at line \fB143\fP of file \fBdlarrk\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.