# Eigenvalues of symmetric tridiagonal interval matrices revisited

## TL;DR

This paper introduces a new, efficient method for accurately computing the bounds of eigenvalues in symmetric tridiagonal interval matrices, avoiding assumptions and explicitly identifying matrices that attain these bounds.

## Contribution

The paper presents a novel, simple, and assumption-free approach for calculating exact eigenvalue bounds of symmetric tridiagonal interval matrices.

## Key findings

- Method is faster and simpler than existing approaches
- Explicitly constructs matrices attaining the bounds
- No assumptions required for the bounds calculation

## Abstract

In this short note, we present a novel method for computing exact lower and upper bounds of eigenvalues of a symmetric tridiagonal interval matrix. Compared to the known methods, our approach is fast, simple to present and to implement, and avoids any assumptions. Our construction explicitly yields those matrices for which particular lower and upper bounds are attained.