A Method of Indefinite Krylov Subspace for Eigenvalue Problem

Eigenvalue Perturbation and Generalized Krylov Subspace Method

In this paper, we study the computational aspect of eigenvalue perturbation theory. In previous research, high order perturbation terms were often derived from Taylor series expansion. Computations based on such an approach can be both unstable and highly complicated. We present here with an approach based on the diierential formulation of perturbation theory where the high order perturbation c...

Generalizations of an Inverse Free Krylov Subspace Method for the Symmetric Generalized Eigenvalue Problem

OF DISSERTATION

The matrix eigenvalue problem - GR and Krylov subspace methods

Scientific Computing, Volume I Germund Dahlquist and Åke Björck This new book from the authors of the highly successful classic Numerical Methods (Prentice-Hall, 1974) addresses the increasingly important role of numerical methods in science and engineering. While treating traditional and well-developed topics, it also emphasizes concepts and ideas of importance to the design of accurate and ef...

Preconditioned Krylov Subspace Methods for Eigenvalue Problems

A Krylov Method for the Delay Eigenvalue Problem

The Arnoldi method is currently a very popular algorithm to solve large-scale eigenvalue problems. The main goal of this paper is to generalize the Arnoldi method to the characteristic equation of a delay-differential equation (DDE), here called a delay eigenvalue problem (DEP). The DDE can equivalently be expressed with a linear infinite dimensional operator whose eigenvalues are the solutions...