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, Vol. 27, No. 1: pp. 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Bavarian Chair for Mathematical Foundations of Artificial Intelligence
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1019-7168
• Language: English