NAME

       slarrk.f -

SYNOPSIS

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

Function/Subroutine Documentation

   subroutine slarrk (integerN, integerIW, realGL, realGU, real, dimension( * )D, real,
       dimension( * )E2, realPIVMIN, realRELTOL, realW, realWERR, integerINFO)
       SLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.

       Purpose:

            SLARRK computes one eigenvalue of a symmetric tridiagonal
            matrix T to suitable accuracy. This is an auxiliary code to be
            called from SSTEMR.

            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 REAL

           GU

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

           D

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

           E2

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

           PIVMIN

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

           RELTOL

                     RELTOL is REAL
                     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 REAL

           WERR

                     WERR is REAL
                     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   REAL            , 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 slarrk.f.

Author

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