|MATLAB Function Reference|
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
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.
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.
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.