The power method for lp norms

AbstractAn iterative method is described which rapidly computes the norm of a nonnegative matrix A, considered as a mapping from the finite dimensional space lr(n) to the space lp(m). In case r=p=2, the method reduces to the familiar power method for determining the largest eigenvalue of the matrix ATA. If the matrix is nonnegative, the method still converges but only to a relative maximum which need not be the norm, in general. A sequence of vectors is also produced which converges to a vector x at which the norm is attained, provided x is a strict nondegenerate maximum