English

The RQR algorithm

Numerical Analysis 2025-04-29 v2 Numerical Analysis

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.

Keywords

Cite

@article{arxiv.2411.17671,
  title  = {The RQR algorithm},
  author = {Daan Camps and Thomas Mach and Raf Vandebril and David S. Watkins},
  journal= {arXiv preprint arXiv:2411.17671},
  year   = {2025}
}

Comments

10 pages, 1 figure