Riemannian Manifold Trust-Region Methods with Applications to Eigenproblems

This thesis presents and evaluates a generic algorithm for incrementally computing the dominant singular subspaces of a matrix. The relationship between the generality of the results and the necessary computation is explored, and it is shown that more efficient computation can be obtained by relaxing the algebraic constraints on the factoriation. The performance of this method, both numerical and computational, is discussed in terms of the algorithmic parameters, such as block size and acceptance threshhold. Bounds on the error are presented along with a posteriori approximations of these bounds. Finally, a group of methods are proposed which iteratively improve the accuracy of computed results and the quality of the bounds.