The aim of this paper is to provide a convergence analysis for a preconditioned subspace iteration, which is designated to determine a modest number of the smallest eigenvalues and its corresponding invariant subspace of eigenvectors of a large, symmetric positive definite matrix. The algorithm is built upon a subspace implementation of preconditioned inverse iteration, i.e., the well-known inv...

The objective in this paper is to present some recent developments regarding the subspace iteration method for the solution of frequencies and mode shapes. The developments pertain to speeding up the basic subspace iteration method by choosing an effective number of iteration vectors and by the use of parallel processing. The subspace iteration method lends itself particularly well to shared an...

Subspace iteration for computing several eigenpairs (i.e. eigenvalues and eigenvectors) of an eigenvalue problem is an alternative to the deflation technique whereby the eigenpairs are computed successively by projecting the problem onto the subspace orthogonal to the already found eigenvectors. The main advantage of the subspace iteration over the deflation is its ‘cluster robustness’: even if...

Global Krylov subspace methods are the most efficient and robust methods to solve generalized coupled Sylvester matrix equation. In this paper, we propose the nested splitting conjugate gradient process for solving this equation. This method has inner and outer iterations, which employs the generalized conjugate gradient method as an inner iteration to approximate each outer iterate, while each...

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 ...