larrk - Man Page

larrk: step in stemr, compute one eigval

subroutine dlarrk (n, iw, gl, gu, d, e2, pivmin, reltol, w, werr, info)
DLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.
subroutine slarrk (n, iw, gl, gu, d, e2, pivmin, reltol, w, werr, info)
SLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.

Detailed Description

Function Documentation

subroutine dlarrk (integer n, integer iw, double precision gl, double precision gu, double precision, dimension( * ) d, double precision, dimension( * ) e2, double precision pivmin, double precision reltol, double precision w, double precision werr, integer info)

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

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.

Parameters

          N is INTEGER
          The order of the tridiagonal matrix T.  N >= 0.

          IW is INTEGER
          The index of the eigenvalues to be returned.

          GL is DOUBLE PRECISION

          GU is DOUBLE PRECISION
          An upper and a lower bound on the eigenvalue.

          D is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the tridiagonal matrix T.

          E2 is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) squared off-diagonal elements of the tridiagonal matrix T.

PIVMIN

          PIVMIN is DOUBLE PRECISION
          The minimum pivot allowed in the Sturm sequence for T.

RELTOL

          RELTOL is 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 is DOUBLE PRECISION

WERR

          WERR is DOUBLE PRECISION
          The error bound on the corresponding eigenvalue approximation
          in W.

INFO

          INFO is INTEGER
          = 0:       Eigenvalue converged
          = -1:      Eigenvalue did NOT converge

Internal Parameters:

  FUDGE   DOUBLE PRECISION, default = 2
          A 'fudge factor' to widen the Gershgorin intervals.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 143 of file dlarrk.f.

subroutine slarrk (integer n, integer iw, real gl, real gu, real, dimension( * ) d, real, dimension( * ) e2, real pivmin, real reltol, real w, real werr, integer info)

SLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.