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# rcond

inverse condition number

### Syntax

`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
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