An effective Lanczos algorithm for large eigenproblems.

Generalized block Lanczos methods for large unsymmetric eigenproblems

Generalized block Lanczos methods for large unsymmetric eigenproblems are presented, which contain the block Arnoldi method, and the block Arnoldi algorithms are developed. The convergence of this class of methods is analyzed when the matrix A is diagonalizable. Upper bounds for the distances between normalized eigenvectors and a block Krylov subspace are derived, and a priori theoretical error...

IRBL: An Implicitly Restarted Block-Lanczos Method for Large-Scale Hermitian Eigenproblems

A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems

An \industrial strength" algorithm for solving sparse symmetric generalized eigenproblems is described. The algorithm has its foundations in known techniques in solving sparse symmetric eigenproblems, notably the spectral transformation of Ericsson and Ruhe and the block Lanczos algorithm. However, the combination of these two techniques is not trivial; there are many pitfalls awaiting the unwa...

A Parallelizable and Fast Algorithm for Very Large Generalized Eigenproblems

We discuss a novel iterative approach for the computation of a number of eigenvalues and eigenvectors of the generalized eigenproblem A x = ABx . Our method is based on a combination of the JacobiDavidson method and the QZ-method. For that reason we refer to the method as JDQZ. The effectiveness of the method is illustrated by a numerical example.

Addendum to "A Krylov-Schur Algorithm for Large Eigenproblems"

In this addendum to an earlier paper by the author, it is shown how to compute a Krylov decomposition corresponding to an arbitrary Rayleigh-Quotient. This decomposition can be used to restart an Arnoldi process, with a selection of the Ritz vectors corresponding to the Rayleigh quotient. ABSTRACT In this addendum to an earlier paper by the author, it is shown how to compute a Krylov decomposit...