slarrk (l)  Linux Man Pages
slarrk: computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy
NAME
SLARRK  computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracySYNOPSIS
 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 (N1)
 The (n1) squared offdiagonal 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.