rcond

Arguments

X

real or complex square matrix

r

real positive number

Description

rcond(X) is an estimate for the reciprocal of the condition of X in the 1-norm.

If X is well conditioned, rcond(X) is close to 1. If not, rcond(X) is close to 0.

Estimating the 1-norm inverse condition number with rcond is much faster than computing the 2-norm condition number with cond. As a trade-off, rcond may be less reliable.

Algorithm: We compute the 1-norm of X with Lapack/DLANGE, compute its LU decomposition with Lapack/DGETRF, and finally estimate the condition with Lapack/DGECON.

rcond([]) yields %inf.

Examples

A = diag([1:10]);
rcond(A)
A(1,1) = 0.000001;
rcond(A)

Comparative benchmark:

A = ones(1000, 1000);
timer(); cond(A);    timer()
timer(); 1/rcond(A); timer()

See also

• svd — singular value decomposition
• cond — condition number of a matrix
• inv — matrix inverse

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