rcond

inverse condition number

Calling Sequence

rcond(X)

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