slarrr (l) - Linux Manuals

slarrr: tests to decide whether the symmetric tridiagonal matrix T warrants expensive computations which guarantee high relative accuracy in the eigenvalues

NAME

SLARRR - tests to decide whether the symmetric tridiagonal matrix T warrants expensive computations which guarantee high relative accuracy in the eigenvalues

SYNOPSIS

SUBROUTINE SLARRR(
N, D, E, INFO )

    
INTEGER N, INFO

    
REAL D( * ), E( * )

PURPOSE

Perform tests to decide whether the symmetric tridiagonal matrix T warrants expensive computations which guarantee high relative accuracy in the eigenvalues.

ARGUMENTS

N (input) INTEGER
The order of the matrix. N > 0.
D (input) REAL array, dimension (N)
The N diagonal elements of the tridiagonal matrix T.
E (input/output) REAL array, dimension (N)
On entry, the first (N-1) entries contain the subdiagonal elements of the tridiagonal matrix T; E(N) is set to ZERO.
INFO (output) INTEGER
INFO = 0(default) : the matrix warrants computations preserving relative accuracy. INFO = 1 : the matrix warrants computations guaranteeing only absolute accuracy.

FURTHER DETAILS

Based on contributions by

Beresford Parlett, University of California, Berkeley, USA
Jim Demmel, University of California, Berkeley, USA

Inderjit Dhillon, University of Texas, Austin, USA

Osni Marques, LBNL/NERSC, USA

Christof Voemel, University of California, Berkeley, USA

Pages related to slarrr

  • slarrr (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,
  • slarrk (l) - computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy
  • 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