Iterative Methods for Computing Eigenvalues and Eigenvectors

TL;DR

This paper reviews various numerical iterative methods for computing eigenvalues and eigenvectors of real matrices, discussing their derivations, procedures, and advantages.

Contribution

It provides a comparative overview of five iterative methods, from simple to complex, for eigenvalue and eigenvector computation.

Findings

Power iteration is simple but slow for multiple eigenvalues.

QR iteration is more efficient for large matrices.

Methods vary in convergence speed and computational complexity.

Abstract

We examine some numerical iterative methods for computing the eigenvalues and eigenvectors of real matrices. The five methods examined here range from the simple power iteration method to the more complicated QR iteration method. The derivations, procedure, and advantages of each method are briefly discussed.