Book Review: The matrix eigenvalue problem: GR and Krylov subspace methods

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

Application of Vector-Valued Rational Approximations to the Matrix Eigenvalue Problem and Connections with Krylov Subspace Methods

Let F(z) be a vector-valued function F C CN, which is analytic at z 0 and meromorphic in a neighborhood of z 0, and let its Maclaurin series be given. In a recent work [J. Approx. Theory, 76 (1994), pp. 89-111] by the author, vector-valued rational approximation procedures for F(z) that are based on its Maclaurin series, were developed, and some of their convergence properties were analyzed in ...

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...

Exploiting Structure in Krylov Subspace Methods for the WilsonFermion Matrix