Condition Number for Matrices from Singular Values
DESCRIPTION:
Computes the reciprocal two-norm condition number for a matrix from its
singular-value decomposition.
USAGE:
rcond.svd.Matrix(x)
REQUIRED ARGUMENTS:
x:
An object of class "svd.Matrix" representing the singular-value
decomposition of a matrix.
VALUE:
A numeric value of class "rcond", representing an estimate of the
reciprocal two norm condition number of the matrix underlying x.
A copy of the call to "rcond" is returned as an attribute.
DETAILS:
The two-norm condition number of a matrix is the ratio of smallest to its
largest magnitude singular values.
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.