Block Krylov–Schur method for large symmetric eigenvalue problems

An Implicitly Restarted Lanczos Method for Large Symmetric Eigenvalue Problems

The Lanczos process is a well known technique for computing a few, say k, eigenvalues and associated eigenvectors of a large symmetric n×n matrix. However, loss of orthogonality of the computed Krylov subspace basis can reduce the accuracy of the computed approximate eigenvalues. In the implicitly restarted Lanczos method studied in the present paper, this problem is addressed by fixing the num...

A block inverse-free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems

Efficiently preconditioned inexact Newton methods for large symmetric eigenvalue problems

Efficiently preconditioned inexact Newton methods for large symmetric eigenvalue problems L. Bergamaschi & A. Martínez a Department of Civil, Environmental and Architectural Engineering, University of Padua, via Trieste 63, 35100 Padova, Italy b Department of Mathematics, University of Padua, via Trieste 63, 35100 Padova, Italy Accepted author version posted online: 14 Apr 2014.Published online...

Harmonic projection methods for large non-symmetric eigenvalue problems

The problem of finding interior eigenvalues of a large nonsymmetric matrix is examined. A procedure for extracting approximate eigenpairs from a subspace is discussed. It is related to the Rayleigh–Ritz procedure, but is designed for finding interior eigenvalues. Harmonic Ritz values and other approximate eigenvalues are generated. This procedure can be applied to the Arnoldi method, to precond...

Inexact Newton Preconditioning Techniques for Large Symmetric Eigenvalue Problems

This paper studies a number of Newton methods and use them to define new secondary linear systems of equations for the Davidson eigenvalue method. The new secondary equations avoid some common pitfalls of the existing ones such as the correction equation and the Jacobi-Davidson preconditioning. We will also demonstrate that the new schemes can be used efficiently in test problems.