slarrk (l) - Linux Manuals

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 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.

Pages related to slarrk

  • slarrk (3)
  • slarra (l) - the splitting points with threshold SPLTOL
  • slarrb (l) - the relatively robust representation(RRR) L D L^T, SLARRB does "limited" bisection to refine the eigenvalues of L D L^T,
  • slarrc (l) - the number of eigenvalues of the symmetric tridiagonal matrix T that are in the interval (VL,VU] if JOBT = aqTaq, and of L D L^T if JOBT = aqLaq
  • slarrd (l) - computes the eigenvalues of a symmetric tridiagonal matrix T to suitable accuracy
  • slarre (l) - find the desired eigenvalues of a given real symmetric tridiagonal matrix T, SLARRE sets any "small" off-diagonal elements to zero, and for each unreduced block T_i, it finds (a) a suitable shift at one end of the blockaqs spectrum,
  • slarrf (l) - the initial representation L D L^T and its cluster of close eigenvalues (in a relative measure), W( CLSTRT ), W( CLSTRT+1 ), ..
  • slarrj (l) - the initial eigenvalue approximations of T, SLARRJ does bisection to refine the eigenvalues of T,
  • slarrr (l) - tests to decide whether the symmetric tridiagonal matrix T warrants expensive computations which guarantee high relative accuracy in the eigenvalues
  • slarrv (l) - computes the eigenvectors of the tridiagonal matrix T = L D L^T given L, D and APPROXIMATIONS to the eigenvalues of L D L^T
  • slar1v (l) - computes the (scaled) r-th column of the inverse of the sumbmatrix in rows B1 through BN of the tridiagonal matrix L D L^T - sigma I