NAME

       dlarrk.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dlarrk (N, IW, GL, GU, D, E2, PIVMIN, RELTOL, W, WERR, INFO)
           DLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable
           accuracy.

Function/Subroutine Documentation

   subroutine dlarrk (integerN, integerIW, double precisionGL, double precisionGU, double
       precision, dimension( * )D, double precision, dimension( * )E2, double precisionPIVMIN,
       double precisionRELTOL, double precisionW, double precisionWERR, integerINFO)
       DLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.

       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.

            See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
            Matrix", Report CS41, Computer Science Dept., Stanford
            University, July 21, 1966.

       Parameters:
           N

                     N is INTEGER
                     The order of the tridiagonal matrix T.  N >= 0.

           IW

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

           GL

                     GL is DOUBLE PRECISION

           GU

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

           D

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

           E2

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

           PIVMIN

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

           RELTOL

                     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

                     W is DOUBLE PRECISION

           WERR

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

           INFO

                     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.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       Definition at line 145 of file dlarrk.f.

Author

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