The finite section method and stable subsequences

• Autores: Marko, Lindner
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 60, Nº. 4, 2010, págs. 501-512
• Idioma: inglés
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• Resumen

  • 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 View the MathML source. 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 Ngreater-or-equal, slanted1; 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 View the MathML source rather than convex polytopes.