Analysis of Subspace Iteration for Eigenvalue Problems with Evolving Matrices

The subspace iteration algorithm, a block generalization of the classical power iteration, is known for its excellent robustness properties. Specifically, the algorithm is resilient to variations in the original matrix, and for this reason it has played an important role in applications ranging from Density Functional Theory in Electronic Structure calculations to matrix completion problems in machine learning, and subspace tracking in signal processing applications. This note explores its convergence properties in the presence of perturbations. The specific question addressed is the following. If we apply the subspace iteration algorithm to a certain matrix and this matrix is perturbed at each step, under what conditions will the algorithm converge?