rcond

Arguments

X

real or complex square matrix

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.

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

Examples

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

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.

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

See also

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