Subspace Acceleration for Large-Scale Parameter-Dependent Hermitian Eigenproblems

A Global Arnoldi Method for Large non-Hermitian Eigenproblems with Special Applications to Multiple Eigenproblems∗

Global projection methods have been used for solving numerous large matrix equations, but nothing has been known on if and how a global projection method can be proposed for solving large eigenproblems. In this paper, based on the global Arnoldi process that generates an Forthonormal basis of a matrix Krylov subspace, a global Arnold method is proposed for large eigenproblems. It computes certa...

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...

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

Spectral recycling strategies for the solution of nonlinear eigenproblems in thermoacoustics

In this work we consider the numerical solution of large nonlinear eigenvalue problems that arise in thermoacoustic simulations involved in the stability analysis of large combustion devices. We briefly introduce the physical modelling that leads to a nonlinear eigenvalue problem that is solved using a nonlinear fixed point iteration scheme. Each step of this nonlinear method requires the solut...

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...