# Numerical computation of formal solutions to interval linear systems of equations

## TL;DR

This paper develops numerical methods using Kaucher interval arithmetic to compute formal solutions of interval linear systems, addressing convergence and implementation challenges.

## Contribution

It introduces two stationary iterative approaches based on matrix splitting for formal solutions in Kaucher arithmetic, comparing their effectiveness.

## Key findings

- Two iterative methods successfully compute formal solutions.
- Convergence conditions are established for the proposed methods.
- Comparison shows advantages over existing approaches.

## Abstract

The work is devoted to the development of numerical methods for computing "formal solutions" of interval systems of linear algebraic equations. These solutions are found in Kaucher interval arithmetic, which extends and completes the classical interval arithmetic algebraically. The need to solve these problems naturally arises, for example, in inner and outer estimation of various solution sets to interval linear systems of equations. The work develops two approaches to the construction of stationary iterative methods for computing the formal solutions that are based on splitting the matrix of the system. We consider their convergence and implementation issues, compare with the other approaches to computing formal solutions.