A minimum norm approach for low-rank approximations of a matrix

The problems of calculating a dominant eigenvector or a dominant pair of singular vectors, arise in several large scale matrix computations. In this paper we propose a minimum norm approach for solving these problems. Given a matrix, AA, the new method computes a rank-one matrix that is nearest to AA, regarding the Frobenius matrix norm. This formulation paves the way for effective minimization techniques. The methods proposed in this paper illustrate the usefulness of this idea. The basic iteration is similar to that of the power method, but the rate of convergence is considerably faster. Numerical experiments are included.