LAPACK 3.11.0
LAPACK: Linear Algebra PACKage

◆ dlarrk()

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.

Download DLARRK + dependencies [TGZ] [ZIP] [TXT]

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
[in]N
          N is INTEGER
          The order of the tridiagonal matrix T.  N >= 0.
[in]IW
          IW is INTEGER
          The index of the eigenvalues to be returned.
[in]GL
          GL is DOUBLE PRECISION
[in]GU
          GU is DOUBLE PRECISION
          An upper and a lower bound on the eigenvalue.
[in]D
          D is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the tridiagonal matrix T.
[in]E2
          E2 is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) squared off-diagonal elements of the tridiagonal matrix T.
[in]PIVMIN
          PIVMIN is DOUBLE PRECISION
          The minimum pivot allowed in the Sturm sequence for T.
[in]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.
[out]W
          W is DOUBLE PRECISION
[out]WERR
          WERR is DOUBLE PRECISION
          The error bound on the corresponding eigenvalue approximation
          in W.
[out]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.