# normest

## Purpose

`Estimate matrix` z``-norm.

## Synopsis

    nrm = normest(S)
    nrm = normest(S,tol)
    [nrm,cnt] = normest(S)

## 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)` is 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,cnt] = normest(S)` also gives the number of power iterations used.

## Examples

The matrix `W = 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 a SPARC 1) 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

    condest, norm, rcond, svd

(c) Copyright 1994 by The MathWorks, Inc.