MATLAB Function Reference
normest

2-norm estimate

Syntax

• ```nrm` `=` `normest(S)
nrm` `=` `normest(S,tol)
[nrm,count] = normest(...)
```

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.

`cond`, `condest`, `norm`, `rcond`, `svd`