  A wide range of problems in computational science and engineering require
estimation of sparse eigenvectors for high dimensional systems. Here, we
propose two variants of the Truncated Orthogonal Iteration to compute multiple
leading eigenvectors with sparsity constraints simultaneously. We establish
numerical convergence results for the proposed algorithms using a perturbation
framework, and extend our analysis to other existing alternatives for sparse
eigenvector estimation. We then apply our algorithms to solve the sparse
principle component analysis problem for a wide range of test datasets, from
simple simulations to real-world datasets including MNIST, sea surface
temperature and 20 newsgroups. In all these cases, we show that the new methods
get state of the art results quickly and with minimal parameter tuning.
