# Single Projection Kaczmarz Extended Algorithms

arXiv: https://arxiv.org/abs/1504.00231 · HTML: https://mlsanity.com/paper/1504.00231/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2015.

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

- [An optimal scheduled learning rate for a randomized Kaczmarz algorithm](https://mlsanity.com/paper/2202.12224/) (2022)
- [Randomized Kaczmarz in Adversarial Distributed Setting](https://mlsanity.com/paper/2302.14615/) (2023)

## Abstract (arXiv)

To find the least squares solution of a very large and inconsistent system of equations, one can employ the extended Kaczmarz algorithm. This method simultaneously removes the error term, such that a consistent system is asymptotically obtained, and applies Kaczmarz iterations for the current approximation of this system. For random corrections of the right hand side and Kaczmarz updates selected at random, convergence to the least squares solution has been shown. We consider the deterministic control strategies, and show convergence to a least squares solution when row and column updates are chosen according to the almost-cyclic or maximal-residual choice.