A method to rigorously enclose eigendecompositions of interval matrices

TL;DR

This paper introduces a rigorous computational method for enclosing eigendecompositions of complex interval matrices using radii polynomials and contraction mapping, ensuring accurate eigenpair bounds.

Contribution

The paper presents a novel method combining radii polynomials and contraction arguments to rigorously enclose eigenpairs of complex interval matrices.

Findings

Effective enclosure of eigenpairs demonstrated

Method ensures rigorous bounds on eigenvalues and eigenvectors

Applicable to complex interval matrices with high reliability

Abstract

In this paper, a rigorous computational method to enclose eigendecompositions of complex interval matrices is proposed. Each eigenpair $x=(\lambda,v)$ is found by solving a nonlinear equation of the form $f(x)=0$ via a contraction argument. The set-up of the method relies on the notion of radii polynomials, which provide an efficient mean of determining a domain on which the contraction mapping theorem is applicable.