The finite section method and stable subsequences
Publikationstyp
Journal Article
Date Issued
2010-04-01
Sprache
English
Author(s)
Volume
60
Issue
4
Start Page
501
End Page
512
Citation
Applied Numerical Mathematics 60 (4): 501-512 (2010-04-01)
Publisher DOI
Scopus ID
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.
Subjects
Band-dominated operator
Finite section method
Projection methods
Stability
DDC Class
510: Mathematik