MATLAB Function Reference |

**Syntax**

**Description**

This function is intended primarily for sparse matrices, although it works correctly and may be useful for large, full matrices as well.

```
nrm = normest(S)
```

returns an estimate of the 2-norm of the matrix `S`

.

```
nrm = normest(S,tol)
```

uses relative error `tol`

instead of the default tolerance `1.e-6`

. The value of `tol`

determines when the estimate is considered acceptable.

```
[nrm,count] = normest(...)
```

returns an estimate of the 2-norm and also gives the number of power iterations used.

**Examples**

The matrix `W = gallery('wilkinson',101)`

is a tridiagonal matrix. Its order, 101, is small enough that `norm(full(W))`

, which involves `svd(full(W))`

, is feasible. The computation takes 4.13 seconds (on one computer) and produces the exact norm, 50.7462. On the other hand, `normest(sparse(W))`

requires only 1.56 seconds and produces the estimated norm, 50.7458.

**Algorithm**

The power iteration involves repeated multiplication by the matrix `S`

and its transpose, `S'`

. The iteration is carried out until two successive estimates agree to within the specified relative tolerance.

**See Also**

`cond`

, `condest`

, `norm`

, `rcond`

, `svd`

norm | notebook |