Computes an estimate of the reciprocal condition number for a real symmetric
and complex Hermitian matrix.
USAGE:
rcond.Hermitian(x, lower=T, tune, workspace)
REQUIRED ARGUMENTS:
x:
A real symmetric or complex Hermitian Matrix inheriting from class "Hermitian".
OPTIONAL ARGUMENTS:
lower:
a logical variable telling whether to use the lower or upper triangle of the
matrix for the factorization used to compute the determinant. The default is
to select the lower triangle.
tune:
a integer vector or list of named tuning parameters that may affect
computational efficiency. The relevant parameters are the blocksize parameters
NB and NBMIN as described in .laenv.
workspace:
workspace provided to the underlying software.
The default is to use the optimum value relative to the tuning parameters.
The optimal workspace for the problem (for the tuning parameters) is
included as part of the output attributes.
VALUE:
A numeric value of class "rcond", representing the reciprocal one or infinity
norm condition estimate.
A copy of the call to "rcond" is returned as an attribute.
DETAILS:
Based on the functions dsytrf, dsycon, zhetrf, zhecon from Lapack
(Anderson et al. (1994)).
The condition number of a square matrix is the product of the norm of that
matrix and the norm of its inverse. Its values fall in the range [1, Inf),
where a value of Inf would imply a singular matrix. A matrix is said to
be ill-conditioned if its has a large condition number. Another way to
view a condition number of a matrix is as a factor by which errors for
solutions to systems of equations with that matrix as coefficient matrix
can be multiplied. Condition numbers usually are estimated rather than
computed exactly for reasons of efficiency.
REFERENCES:
Anderson, E., et al. (1994).
LAPACK User's Guide,
2nd edition, SIAM, Philadelphia.
Golub, G., and Van Loan, C. F. (1989).
Matrix Computations,
2nd edition, Johns Hopkins, Baltimore.