# On Remotest set and Random controls in Kaczmarz algorithm

## TL;DR

This paper analyzes the Kaczmarz algorithm with Remotest set and Random control, providing conditions ensuring each index appears infinitely often during iterations, which enhances understanding of its convergence behavior.

## Contribution

It introduces a sufficient condition for the recurrence of projection indices in the Kaczmarz algorithm with specific control strategies.

## Key findings

- Provided a sufficient condition for index recurrence in the algorithm.
- Enhanced understanding of convergence properties under Remotest set and Random control.
- Contributed to the theoretical analysis of the Kaczmarz method.

## Abstract

In this paper we analyse the Kaczmarz projection algorithm with Remotest set and Random control of projection indices and provide a sufficient condition such that each projection index appears infinitely many times during the iterations.