# Randomized Extended Kaczmarz is a Limit Point of Sketch-and-Project

@article{Jarman2021RandomizedEK, title={Randomized Extended Kaczmarz is a Limit Point of Sketch-and-Project}, author={Benjamin P. Jarman and Nathan Mankovich and Jacob D. Moorman}, journal={ArXiv}, year={2021}, volume={abs/2110.05605} }

The sketch-and-project (SAP) framework for solving systems of linear equations has unified the theory behind popular projective iterative methods such as randomized Kaczmarz, randomized coordinate descent, and variants thereof. The randomized extended Kaczmarz (REK) method is a popular extension of randomized Kaczmarz for solving inconsistent systems, which has not yet been shown to lie within the SAP framework. In this work we show that, in a certain sense, REK may be expressed as the limit…

## One Citation

A deterministic Kaczmarz algorithm for solving linear systems

- Mathematics, Computer ScienceArXiv
- 2021

It is proved that taking the average of O(η/ǫ) points leads to an effective approximation of the solution up to relative error ǫ, where η is a parameter depending on A and can be bounded above by the square of the condition number.

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