SLARRK(1) LAPACK auxiliary routine (version 3.2) SLARRK(1)NAME
SLARRK - 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 eigen‐
value.
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., con‐
verged. 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.
LAPACK auxiliary routine (versioNovember 2008 SLARRK(1)
