NAME¶

DLARRK - computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy

SYNOPSIS¶

SUBROUTINE DLARRK(

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

IMPLICIT NONE INTEGER INFO, IW, N DOUBLE PRECISION PIVMIN, RELTOL, GL, GU, W, WERR DOUBLE PRECISION D( * ), E2( * )

PURPOSE¶

DLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy. This is an auxiliary code to be called from DSTEMR.
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) DOUBLE PRECISION

GU (input) DOUBLE PRECISION An upper and a lower bound on the eigenvalue.

D (input) DOUBLE PRECISION array, dimension (N)

The n diagonal elements of the tridiagonal matrix T.

E2 (input) DOUBLE PRECISION array, dimension (N-1)

The (n-1) squared off-diagonal elements of the tridiagonal matrix T.

PIVMIN (input) DOUBLE PRECISION

The minimum pivot allowed in the Sturm sequence for T.

RELTOL (input) DOUBLE PRECISION

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) DOUBLE PRECISION

WERR (output) DOUBLE PRECISION

The error bound on the corresponding eigenvalue approximation in W.

INFO (output) INTEGER

= 0: Eigenvalue converged
= -1: Eigenvalue did NOT converge

PARAMETERS¶

FUDGE DOUBLE PRECISION, default = 2

A "fudge factor" to widen the Gershgorin intervals.