Iterations of the generalized Gram-Schmidt procedure for generating Parseval frames
Tomislav Beri\'c
TL;DR
This paper explores the properties and iterative behavior of the generalized Gram-Schmidt procedure (GGSP) for creating Parseval frames, including its limits and practical examples.
Contribution
It analyzes the iterative process of GGSP, providing insights into its convergence and characteristics, which were not previously detailed.
Findings
Properties of the GGSP are characterized.
The limit of the iterative procedure is investigated.
Examples illustrate the behavior of the iterated process.
Abstract
In this paper we describe some properties of the generalized Gram-Schmidt procedure (GGSP) for generating Parseval frames which was first introduced by Casazza and Kutyniok [A generalization of Gram-Schmidt orthogonalization generating all Parseval frames, Adv. Comput. Math. 27 (2007), pp. 65-78]. Next we investigate the iterations of the procedure and its limit. In the end we give some examples of the iterated procedure.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Digital Filter Design and Implementation · Advanced Numerical Analysis Techniques