`normest`

Estimate of the 2-norm of a matrix.

Syntax

n = normest(S)

Estimates norm(S) to a default relative tolerance of 1e-6.

n = normest(S, tol)

Uses the relative tolerance tol.

Description

normest runs the power method on S'*S, which only needs products of S with vectors. It avoids the full singular value decomposition that norm(S) performs, so it scales to sparse matrices that are too large to factor.

The estimate converges from below, and a tighter tol costs more iterations.

Input arguments

S: Matrix, often large and sparse.
tol: Relative tolerance for the iteration.

Output arguments

n: Approximation of the largest singular value of S.

Example

Estimate against the exact norm

A = magic(4);
normest(A)
norm(A)

Output

ans = 34
ans = 34

normest