# Comparison results for Proper Double Splittings of Rectangular Matrices

## TL;DR

This paper investigates proper double splittings of semi-monotone rectangular matrices to derive comparison results for spectral radii, aiding in analyzing the convergence rates of iterative methods for solving linear systems.

## Contribution

It introduces new comparison results for spectral radii of iteration matrices from proper double splittings of rectangular matrices, enhancing convergence analysis.

## Key findings

- Derived new spectral radius comparison results
- Provided insights into convergence rates of iterative methods
- Applicable to semi-monotone rectangular matrices

## Abstract

In this article, we consider two proper double splittings satisfying certain conditions, of a semi-monotone rectangular matrix A and derive new comparison results for the spectral radii of the correspond ing iteration matrices. These comparison results are useful to analyse the rate of convergence of the iterative methods (formulated from the double splittings) for solving rectangular linear system Ax = b.