# A New Cyclic Gradient Method Adapted to Large-Scale Linear Systems

## TL;DR

This paper introduces a novel cyclic gradient method tailored for large-scale linear systems, demonstrating finite termination in two dimensions and linear convergence in higher dimensions, with practical advantages shown through experiments.

## Contribution

The paper presents a new gradient algorithm with proven finite termination in 2D and linear convergence in higher dimensions, outperforming existing methods in large-scale problems.

## Key findings

- Finite termination in two dimensions.
- R-linear convergence in any dimension.
- Outperforms existing methods in large-scale experiments.

## Abstract

This paper proposes a new gradient method to solve the large-scale problems. Theoretical analysis shows that the new method has finite termination property for two dimensions and converges R-linearly for any dimensions. Experimental results illustrate first the issue of parallel implementation. Then, the solution of a large-scale problem shows that the new method is better than the others, even competitive with the conjugate gradient method.