Publisher DOI: 10.1016/j.apnum.2009.11.006
Title: The finite section method and stable subsequences
Language: English
Authors: Lindner, Marko  
Keywords: Band-dominated operator; Finite section method; Projection methods; Stability
Issue Date: 1-Apr-2010
Source: Applied Numerical Mathematics 60 (4): 501-512 (2010-04-01)
Abstract (english): 
The purpose of this paper is to prove a sufficient and necessary criterion on the stability of a subsequence of the finite section method for a so-called band-dominated operator on ℓp (ZN, X). We hereby generalize previous results into several directions: We generalize the subsequence theorem from dimension N = 1 (see Rabinovich, Roch and Silbermann (2008) [18]) to arbitrary dimensions N ≥ 1; and even for the case of the full sequence, our result is new in dimensions N > 2 and it corrects a mistake in the literature for N = 2. Moreover, we allow the truncations to be taken by homothetic copies of very general starlike geometries Ω ∈ RN rather than convex polytopes. © 2009 IMACS.
URI: http://hdl.handle.net/11420/10588
ISSN: 0168-9274
Journal: Applied numerical mathematics 
Document Type: Article
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