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.