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A Kaczmarz algorithm for sequences of projections, infinite products, and applications to frames in IFS L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{2}$$\end{document} spaces

A Kaczmarz algorithm for sequences of projections, infinite products, and applications to frames... We show that an idea, originating initially with a fundamental recursive iteration scheme (usually referred as “the” Kaczmarz algorithm), admits important applications in such infinite-dimensional, and non-commutative, settings as are central to spectral theory of operators in Hilbert space, to optimization, to large sparse systems, to iterated function systems (IFS), and to fractal harmonic analysis. We present a new recursive iteration scheme involving as input a prescribed sequence of selfadjoint projections. Applications include random Kaczmarz recursions, their limits, and their error-estimates. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Operator Theory Springer Journals

A Kaczmarz algorithm for sequences of projections, infinite products, and applications to frames in IFS L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{2}$$\end{document} spaces

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Publisher
Springer Journals
Copyright
Copyright © Tusi Mathematical Research Group (TMRG) 2020
ISSN
2662-2009
eISSN
2538-225X
DOI
10.1007/s43036-020-00079-1
Publisher site
See Article on Publisher Site

Abstract

We show that an idea, originating initially with a fundamental recursive iteration scheme (usually referred as “the” Kaczmarz algorithm), admits important applications in such infinite-dimensional, and non-commutative, settings as are central to spectral theory of operators in Hilbert space, to optimization, to large sparse systems, to iterated function systems (IFS), and to fractal harmonic analysis. We present a new recursive iteration scheme involving as input a prescribed sequence of selfadjoint projections. Applications include random Kaczmarz recursions, their limits, and their error-estimates.

Journal

Advances in Operator TheorySpringer Journals

Published: Jul 25, 2020

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