### Abstract

Eigenvalue computations are ubiquitous in science and engineering. John Francis’s implicitly shifted QR algorithm has been the method of choice for small to medium sized eigenvalue problems since its invention in 1959. This book presents a new view of this classical algorithm. While Francis’s original procedure chases bulges, the new version chases core transformations, which allows the development of fast algorithms for eigenvalue problems with a variety of special structures. This also leads to a fast and backward stable algorithm for computing the roots of a polynomial by solving the companion matrix eigenvalue problem. The authors received a SIAM Outstanding Paper prize for this work.

Original language | English |
---|---|

Publisher | Society of Industrial and Applied Mathematics |

Number of pages | 149 |

ISBN (Electronic) | 978-1-61197-534-5 |

ISBN (Print) | 978-1-611975-33-8 |

Publication status | Published - Jul 2018 |

### Publication series

Name | Fundamentals of Algorithms |
---|

## Fingerprint Dive into the research topics of 'Core Chasing Algorithms for the Eigenvalue Problem'. Together they form a unique fingerprint.

## Cite this

Aurentz, J. L., Mach, T., Robol, L., Vandebril, R., & Watkins, D. S. (2018).

*Core Chasing Algorithms for the Eigenvalue Problem*. (Fundamentals of Algorithms). Society of Industrial and Applied Mathematics.