MATLAB Function Reference    

2-norm estimate



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.


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.


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