A Jacobi–Davidson Method for Nonlinear Eigenproblems

Abstract

Abstract. For the nonlinear eigenvalue problem T (λ)x = 0 we consider a Jacobi-Davidson type iterative projection method. The resulting projected nonlinear eigenvalue problems are solved by inverse iteration. The method is applied to a rational eigenvalue problem governing damped vibrations of a structure.

Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods

“…A natural generalization of the Jacobi-Davidson method for linear eigenproblems which was already suggested in [92,95] for polynomial eigenvalue problems and which was studied in [15,110] for general nonlinear eigenproblems is the following one: Suppose that the columns of V ⊂ C n form an orthonormal basis of the current search space, and let (x, θ) be a Ritz pair of (1) with respect to V , i.e. V H F (θ)V y = 0, x = V y.…”

Jacobi-Davidson iteration based reduced order finite element models for radar cross-section

“…The use of a preconditioned iterative solver would accelerate this process even further. A detailed explanation of this algorithm can be found in [5].…”

“…This paper proposes to use the Jacobi-Davidson algorithm [5] to extract the eigenspace structure which is then used to generate a reduced order model of a large-scale plane wave scattering problem. This reduced order model is then used to expediently compute radar cross-sections (RCS).…”

Data Clustering with Quantum Mechanics

“…Similar to the Lanczos' method, Davidson's method is an iterative projection method that however does not take advantage of Krylov subspaces, but uses the Rayleigh-Ritz procedure with non-Krylov spaces and expands the search spaces in a different way. It has been successfully applied to ab initio quantum chemistry calculations [33]. The best and most general eigenpair solver using the Jacobi-Davidson scheme is the PRIMMEcode [34], and it is amenable to parallel processing.…”