Mathematics > Numerical Analysis
[Submitted on 18 Dec 2018 (v1), last revised 10 Oct 2019 (this version, v3)]
Title:The infinite Lanczos method for symmetric nonlinear eigenvalue problems
View PDFAbstract:A new iterative method for solving large scale symmetric nonlinear eigenvalue problems is presented. We firstly derive an infinite dimensional symmetric linearization of the nonlinear eigenvalue problem, then we apply the indefinite Lanczos method to this specific linearization, resulting in a short-term recurrence. We show how, under specific assumption on the starting vector, this method can be carried out in finite arithmetic and how the exploitation of the problem structure leads to improvements in terms of computation time. The eigenpair approximations are extracted with the nonlinear Rayleigh-Ritz procedure combined with a specific choice of the projection space. We illustrate how this extraction technique resolves the instability issues that may occur due to the loss of orthogonality in many standard Lanczos-type methods.
Submission history
From: Giampaolo Mele [view email][v1] Tue, 18 Dec 2018 18:41:46 UTC (604 KB)
[v2] Sat, 26 Jan 2019 14:15:08 UTC (610 KB)
[v3] Thu, 10 Oct 2019 09:54:36 UTC (394 KB)
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