The infinite Lanczos method for symmetric nonlinear eigenvalue problems

Abstract A new iterative method for solving large scale symmetric nonlinear eigenvalue problems is presented. We firstly derive an infinite dimensional linearization of the problem, then we apply indefinite Lanczos to this specific linearization, resulting in a short-term recurrence. show how, under assumption on starting vector, can be carried out finite arithmetic and how exploitation problem structure leads improvements terms computation time. The eigenpair approximations are extracted with Rayleigh-Ritz procedure combined choice projection space. illustrate extraction technique resolves instability issues that may occur due loss orthogonality many standard Lanczos-type methods.