Gershgorin disk theorem in complex interval matrices

S Chakraverty,S Maiti

doi:10.3176/proc.2022.1.06

Abstract

Gershgorin disk theorem in complex interval matrices

Highlights

Finding eigenvalues of matrices is a fundamental problem in linear algebra, and it concerns numerous issues of engineering computations
We have proposed theorems based on the Gershgorin disk theorem that can bound separately real and imaginary parts of eigenvalues of complex interval matrices
If we observe the behavioural changes of the Gershgorin disk theorem on complex interval matrices for enclosing complex interval eigenvalues, we can see that for diagonal interval matrices Rohn [9], Hertz [14], and the Gershgorin disk theorem have provided the same interval eigenvalue bounds

Summary

Introduction

Finding eigenvalues of matrices is a fundamental problem in linear algebra, and it concerns numerous issues of engineering computations. The bounded uncertain error appears and influences us to calculate interval eigenvalues of interval matrices. Computing exact eigenvalue bounds for interval matrices is a challenging task. To determine the stability of the uncertain dynamical systems, we need to compute tighter interval eigenvalue bounds of interval matrices that appear in uncertain dynamical systems [1]. Stability analysis of a fractional-order linear time-invariant uncertain system can be performed by calculating eigenvalues of Hermitian complex interval matrix as shown by Ahn et al [3]. Other applications of computing tighter eigenvalue bounds of interval matrices correlated to the problems with bounded uncertainty are a spring-mass system [4,5], a nine-bar truss [4], etc

Objectives

Discussion

Conclusion