| larrk(3) | LAPACK | larrk(3) |
larrk - 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.
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
IW is INTEGER
The index of the eigenvalues to be returned.
GL
GL is DOUBLE PRECISION
GU
GU is DOUBLE PRECISION
An upper and a lower bound on the eigenvalue.
D
D is DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the tridiagonal matrix T.
E2
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
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
SLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.
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.
Parameters
N is INTEGER
The order of the tridiagonal matrix T. N >= 0.
IW
IW is INTEGER
The index of the eigenvalues to be returned.
GL
GL is REAL
GU
GU is REAL
An upper and a lower bound on the eigenvalue.
D
D is REAL array, dimension (N)
The n diagonal elements of the tridiagonal matrix T.
E2
E2 is REAL array, dimension (N-1)
The (n-1) squared off-diagonal elements of the tridiagonal matrix T.
PIVMIN
PIVMIN is REAL
The minimum pivot allowed in the Sturm sequence for T.
RELTOL
RELTOL is 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
W is REAL
WERR
WERR is REAL
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 REAL , default = 2
A 'fudge factor' to widen the Gershgorin intervals.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Generated automatically by Doxygen for LAPACK from the source code.
| Thu Aug 7 2025 17:26:25 | Version 3.12.0 |