Condition Estimation for Triangular Matrices
DESCRIPTION:
Computes an estimate of the reciprocal condition number of a triangular matrix.
USAGE: 
rcond.LowerTriangular(x, one.norm=T)
rcond.UpperTriangular(x, one.norm=T)
rcond.UnitLowerTriangular(x, one.norm=T)
rcond.UnitUpperTriangular(x, one.norm=T)
REQUIRED ARGUMENTS:
x:
A triangular Matrix, that is a matrix inheriting from class "Matrix" and one of "LowerTriangular", "UpperTriangular", "UnitLowerTriangular", or "UnitUpperTriangular".
OPTIONAL ARGUMENTS:
one.norm:
A logical variable which indicates computation of the 1-norm condition estimate if TRUE and the infinity-norm condition estimate otherwise.
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:
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:
Golub, G., and Van Loan, C. F. (1989). Matrix Computations, 2nd edition, Johns Hopkins, Baltimore.
SEE ALSO:
rcond.Matrix
EXAMPLES: 
x <- Matrix( sample(-3:3, size = 9, replace = T), nrow = 3, ncol = 3)
x[row(x) > col(x)] <- 0        # construct triangular matrix
class(x) <- Matrix.class(x)
rcond(x, one.norm = T)
rcond(x, one.norm = F)