 SLARRK(3) computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy

## SYNOPSIS

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

IMPLICIT NONE

INTEGER INFO, IW, N

REAL PIVMIN, RELTOL, GL, GU, W, WERR

REAL D( * ), E2( * )

## 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.

## ARGUMENTS

N (input) INTEGER
The order of the tridiagonal matrix T. N >= 0.
IW (input) INTEGER
The index of the eigenvalues to be returned.
GL (input) REAL
GU (input) REAL An upper and a lower bound on the eigenvalue.
D (input) REAL array, dimension (N)
The n diagonal elements of the tridiagonal matrix T.
E2 (input) REAL array, dimension (N-1)
The (n-1) squared off-diagonal elements of the tridiagonal matrix T.
PIVMIN (input) REAL
The minimum pivot allowed in the Sturm sequence for T.
RELTOL (input) 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 (output) REAL
WERR (output) REAL
The error bound on the corresponding eigenvalue approximation in W.
INFO (output) INTEGER
= 0: Eigenvalue converged
= -1: Eigenvalue did NOT converge

## PARAMETERS

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