# A Kaczmarz algorithm for sequences of projections, infinite products, and applications to frames in IFS L2 spaces

arXiv: https://arxiv.org/abs/1904.04414 · HTML: https://mlsanity.com/paper/1904.04414/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Apr 2019.

## Built on by (most cited first, 2 of 2)

- [Infinite-Dimensional Operator/Block Kaczmarz Algorithms: Regret Bounds and λ-Effectiveness](https://mlsanity.com/paper/2511.07604/) (2025)
- [Use of operator defect identities in multi-channel signal plus residual-analysis via iterated products and telescoping energy-residuals: Applications to kernels in machine learning](https://mlsanity.com/paper/2601.18080/) (2026)

## Abstract (arXiv)

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.