On Variations of Power Iteration

The power iteration is a classical method for computing the eigenvector associated with the largest eigenvalue of a matrix. The subspace iteration is an extension of the power iteration where the subspace spanned by n largest eigenvectors of a matrix, is determined. The natural power iteration is an exemplary instance of the subspace iteration, providing a general framework for many principal subspace algorithms. In this paper we present variations of the natural power iteration, where n largest eigenvectors of a symmetric matrix without rotation ambiguity are determined, whereas the subspace iteration or the natural power iteration finds an invariant subspace (consisting of rotated eigenvectors). The resulting method is referred to as constrained natural power iteration and its fixed point analysis is given. Numerical experiments confirm the validity of our algorithm.