DLARRK(3)      LAPACK routine of NEC Numeric Library Collection      DLARRK(3)



NAME
       DLARRK

SYNOPSIS
       SUBROUTINE DLARRK (N, IW, GL, GU, D, E2, PIVMIN, RELTOL, W, WERR, INFO)



PURPOSE
            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.





ARGUMENTS
           N         (input)
                     N is INTEGER
                     The order of the tridiagonal matrix T.  N >= 0.

           IW        (input)
                     IW is INTEGER
                     The index of the eigenvalues to be returned.

           GL        (input)
                     GL is DOUBLE PRECISION

           GU        (input)
                     GU is DOUBLE PRECISION
                     An upper and a lower bound on the eigenvalue.

           D         (input)
                     D is DOUBLE PRECISION array, dimension (N)
                     The n diagonal elements of the tridiagonal matrix T.

           E2        (input)
                     E2 is DOUBLE PRECISION array, dimension (N-1)
                     The (n-1) squared off-diagonal elements of the tridiagonal matrix T.

           PIVMIN    (input)
                     PIVMIN is DOUBLE PRECISION
                     The minimum pivot allowed in the Sturm sequence for T.

           RELTOL    (input)
                     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.

           W         (output)
                     W is DOUBLE PRECISION

           WERR      (output)
                     WERR is DOUBLE PRECISION
                     The error bound on the corresponding eigenvalue approximation
                     in W.

           INFO      (output)
                     INFO is INTEGER
                     = 0:       Eigenvalue converged
                     = -1:      Eigenvalue did NOT converge



       Internal Parameters:


             FUDGE   DOUBLE PRECISION, default = 2
                     A "fudge factor" to widen the Gershgorin intervals.



LAPACK routine                  31 October 2017                      DLARRK(3)