Large sparse Hamiltonian eigenvalue problems arise in a variety of contexts. These problems can be attacked directly, or they can rst be transformed to problems having some related structure, such as symplectic or skew Hamiltonian. In the interest of eciency, stability, and accuracy, such problems should be solved by methods that preserve the structure, whether it be Hamiltonian, skew Hamiltonian, or symplectic.

A Hamiltonian Krylov-Schur-type method based on the symplectic

Abstract. We investigate the long-term behavior of the classical Lanczos process in an attempt to pave the way to an ecient and robust eigensolver that can nd all the eigenvalues of large sparse symmetric matrices. We are interested in the convergence of classical Lanczos (i.e., without re

. Krylov subspace based moment matching algorithms, such as PVL (Pade approximation Via the Lanczos process), have emerged as popular tools for efficient analyses of the impulse response in a large linear circuit. In this work, a new derivation of the PVL algorithm is presented from the matrix

For the eigenvalues of a large and sparse unsymmetric coefficient matrix, we propose an improved version of the unsymmetric Lanczos process combining elements of numerical stability and parallel algorithm design. Stability is obtained by a coupled two-term recurrences procedure that generates

. For the eigenvalues of a large and sparse unsymmetric coefficient matrix, we have proposed an improved version of the unsymmetric Lanczos process combining elements of numerical stability and parallel algorithm design. The algorithm is derived such that all inner products and matrix

... to compute a QR decomposition of a tridiagonal coefficient matrix gained in the Lanczos process. This QR decomposition is constructed by an update scheme applying in every step a single Givens rotation. Using complex Householder reflections we generalize this idea to block tridiagonal matrices

Abstract. Krylov subspace based moment matching algorithms, such as PVL (Padé approximation Via the Lanczos process), have emerged as popular tools for efficient analyses of the impulse response in a large linear circuit. In this work, a new derivation of the PVL algorithm is presented from

. The paper introduces PVLß, an algorithm for computing partial Padé-based reduced-order models via the Lanczos process. The effectiveness of this modeling methodology is illustrated by numerical examples.

Abstract. The symmetric band Lanczos process is an extension of the classical Lanczos algorithm for symmetric matrices and single starting vectors to multiple starting vectors. After n iterations, the symmetric band Lanczos process has generated an n × n projection, Ts n, of the given symmetric