Strict localization of eigenvectors and eigenvalues

TL;DR

This paper introduces a simple, efficient method based on the modified cone condition for precisely locating eigenvectors and eigenvalues of matrices, with applications to zero localization of complex polynomials.

Contribution

The paper presents a novel, straightforward approach for strict localization of eigenvectors and eigenvalues using the modified cone condition, enhancing precision and computational efficiency.

Findings

Effective eigenvalue and eigenvector localization demonstrated

Method also localizes zeros of complex polynomials

Implementation confirms practical utility

Abstract

In this article we show and implement a simple and effcient method to strictly locate eigenvectors and eigenvalues of a given matrix, based on the modified cone condition. As a consequence we can also effectively localize zeros of complex polynomials.