Journal article
A Kaczmarz algorithm for sequences of projections, infinite products, and applications to frames in IFS L2 spaces
Advances in operator theory, Vol.5(3), pp.1100-1131
05/25/2020
DOI: 10.1007/s43036-020-00079-1
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.
Details
- Title: Subtitle
- A Kaczmarz algorithm for sequences of projections, infinite products, and applications to frames in IFS L2 spaces
- Creators
- Palle Jorgensen - University of IowaMyung-Sin Song - Southern Illinois University EdwardsvilleJames Tian - Mathematical Reviews
- Resource Type
- Journal article
- Publication Details
- Advances in operator theory, Vol.5(3), pp.1100-1131
- Publisher
- Springer International Publishing
- DOI
- 10.1007/s43036-020-00079-1
- ISSN
- 2662-2009
- eISSN
- 2538-225X
- Language
- English
- Date published
- 05/25/2020
- Academic Unit
- Mathematics
- Record Identifier
- 9984241040702771
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