A generalization of Gram–Schmidt orthogonalization generating all Parseval frames

Casazza, Peter G. und Kutyniok, Gitta (30. November 2007): A generalization of Gram–Schmidt orthogonalization generating all Parseval frames. In: Advances in Computational Mathematics, Bd. 27, Nr. 1: S. 65-78

Abstract

Given an arbitrary finite sequence of vectors in a finite-dimensional Hilbert space, we describe an algorithm, which computes a Parseval frame for the subspace generated by the input vectors while preserving redundancy exactly. We further investigate several of its properties. Finally, we apply the algorithm to several numerical examples.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Professur für Mathematische Grundlagen des Verständnisses der künstlichen Intelligenz
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 1019-7168
• Sprache: Englisch