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.

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

  FUDGE   REAL            , default = 2


          A "fudge factor" to widen the Gershgorin intervals.

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September 2012