Subspace Acceleration for Large-Scale Parameter-Dependent Hermitian Eigenproblems

Subspace Acceleration for Large-Scale Parameter-Dependent Hermitian Eigenproblems

This work is concerned with approximating the smallest eigenvalue of a parameterdependent Hermitian matrix A(μ) for many parameter values μ ∈ R . The design of reliable and efficient algorithms for addressing this task is of importance in a variety of applications. Most notably, it plays a crucial role in estimating the error of reduced basis methods for parametrized partial differential equati...

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

Preconditioned Eigensolvers for Large-Scale Nonlinear Hermitian Eigenproblems with Variational Characterizations. II. Interior Eigenvalues

We consider the solution of large-scale nonlinear algebraic Hermitian eigenproblems of the form T (λ)v = 0 that admit a variational characterization of eigenvalues. These problems arise in a variety of applications and are generalizations of linear Hermitian eigenproblems Av=λBv. In this paper, we propose a Preconditioned Locally Minimal Residual (PLMR) method for efficiently computing interior...

Preconditioned Eigensolvers for Large-scale Nonlinear Hermitian Eigenproblems with Variational Characterizations. I. Conjugate Gradient Methods

Preconditioned conjugate gradient (PCG) methods have been widely used for computing a few extreme eigenvalues of large-scale linear Hermitian eigenproblems. In this paper, we study PCG methods to compute extreme eigenvalues of nonlinear Hermitian eigenproblems of the form T (λ)v = 0 that admit a nonlinear variational principle. We investigate some theoretical properties of a basic CG method, in...

Subspace Iteration for Eigenproblems

We discuss a novel approach for the computation of a number of eigenvalues and eigenvectors of the standard eigenproblem Ax = x. Our method is based on a combination of the Jacobi-Davidson method and the QR-method. For that reason we refer to the method as JDQR. The eeectiveness of the method is illustrated by a numerical example.