The RQR algorithm

TL;DR

This paper introduces a pole-swapping algorithm for solving the standard eigenvalue problem, offering a competitive alternative to the traditional QR algorithm.

Contribution

It presents a novel pole-swapping algorithm specifically designed for the standard eigenvalue problem, extending the concept from generalized eigenvalue problems.

Findings

The pole-swapping algorithm is competitive with the QR algorithm.

It provides an alternative approach to eigenvalue computation.

The algorithm generalizes pole-swapping techniques to the standard eigenproblem.

Abstract

Pole-swapping algorithms, generalizations of bulge-chasing algorithms, have been shown to be a viable alternative to the bulge-chasing QZ algorithm for solving the generalized eigenvalue problem for a matrix pencil A - {\lambda}B. It is natural to try to devise a pole-swapping algorithm that solves the standard eigenvalue problem for a single matrix A. This paper introduces such an algorithm and shows that it is competitive with Francis's bulge-chasing QR algorithm.