A New Operator and Method for Solving Interval Linear Equations

TL;DR

This paper introduces a novel operator and an associated algorithm for solving interval linear equations, improving efficiency and accuracy over classical methods through numerical validation.

Contribution

It presents a new operator generalizing the interval Gauss-Seidel method and a magnitude method algorithm that enhances solution sharpness and computational speed.

Findings

Outperforms classical methods in numerical examples

Provides sharper enclosures of solutions

Reduces computational time

Abstract

We deal with interval linear systems of equations. We present a new operator, which generalizes the interval Gauss-Seidel method. Also, based on the new operator and properties of the well-known methods, we propose a new algorithm, called the magnitude method. We illustrate by numerical examples that our approach overcomes some classical methods with respect to both time and sharpness of enclosures.