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 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.