.TH SLARRK 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) "
.SH NAME
SLARRK - one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy
.SH SYNOPSIS
.TP 19
SUBROUTINE SLARRK(
N, IW, GL, GU,
D, E2, PIVMIN, RELTOL, W, WERR, INFO)
.TP 19
.ti +4
IMPLICIT
NONE
.TP 19
.ti +4
INTEGER
INFO, IW, N
.TP 19
.ti +4
REAL
PIVMIN, RELTOL, GL, GU, W, WERR
.TP 19
.ti +4
REAL
D( * ), E2( * )
.SH PURPOSE
SLARRK computes one eigenvalue of a symmetric tridiagonal
matrix T to suitable accuracy. This is an auxiliary code to be
called from SSTEMR.
.br
To avoid overflow, the matrix must be scaled so that its
.br
largest element is no greater than overflow**(1/2) *
.br
underflow**(1/4) in absolute value, and for greatest
.br
accuracy, it should not be much smaller than that.
.br
See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
Matrix", Report CS41, Computer Science Dept., Stanford
.br
University, July 21, 1966.
.br
.SH ARGUMENTS
.TP 8
N (input) INTEGER
The order of the tridiagonal matrix T. N >= 0.
.TP 8
IW (input) INTEGER
The index of the eigenvalues to be returned.
.TP 8
GL (input) REAL
GU (input) REAL
An upper and a lower bound on the eigenvalue.
.TP 8
D (input) REAL array, dimension (N)
The n diagonal elements of the tridiagonal matrix T.
.TP 8
E2 (input) REAL array, dimension (N-1)
The (n-1) squared off-diagonal elements of the tridiagonal matrix T.
.TP 8
PIVMIN (input) REAL
The minimum pivot allowed in the Sturm sequence for T.
.TP 8
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.
.TP 8
W (output) REAL
.TP 8
WERR (output) REAL
The error bound on the corresponding eigenvalue approximation
in W.
.TP 8
INFO (output) INTEGER
= 0: Eigenvalue converged
.br
= -1: Eigenvalue did NOT converge
.SH PARAMETERS
.TP 8
FUDGE REAL , default = 2
A "fudge factor" to widen the Gershgorin intervals.