A Kaczmarz algorithm for sequences of projections, infinite products, and applications to frames in IFS $L^{2}$ spaces
Functional Analysis
2019-04-10 v1 Numerical Analysis
Optimization and Control
Probability
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.
Keywords
Cite
@article{arxiv.1904.04414,
title = {A Kaczmarz algorithm for sequences of projections, infinite products, and applications to frames in IFS $L^{2}$ spaces},
author = {Palle Jorgensen and Myung-Sin Song and Feng Tian},
journal= {arXiv preprint arXiv:1904.04414},
year = {2019}
}