### Abstract

The following problem is addressed: given square matrices A and B, compute the smallest ε such that A + E and B + F have a common eigenvalue for some E, F with max(∥E∥, ∥F∥^{2}) ≤ ε. An algorithm to compute this quantity to any prescribed accuracy is presented, assuming that eigenvalues can be computed exactly.

Original language | English (US) |
---|---|

Pages (from-to) | 348-359 |

Number of pages | 12 |

Journal | SIAM Journal on Matrix Analysis and Applications |

Volume | 28 |

Issue number | 2 |

DOIs | |

State | Published - 2006 |

### Fingerprint

### Keywords

- Eigenvalue perturbation
- Eigenvalue separation
- Pencil
- Pseudospectra

### ASJC Scopus subject areas

- Algebra and Number Theory
- Applied Mathematics
- Analysis

### Cite this

*SIAM Journal on Matrix Analysis and Applications*,

*28*(2), 348-359. https://doi.org/10.1137/050622584

**An algorithm to compute sepλ.** / Gu, Ming; Overton, Michael L.

Research output: Contribution to journal › Article

*SIAM Journal on Matrix Analysis and Applications*, vol. 28, no. 2, pp. 348-359. https://doi.org/10.1137/050622584

}

TY - JOUR

T1 - An algorithm to compute sepλ

AU - Gu, Ming

AU - Overton, Michael L.

PY - 2006

Y1 - 2006

N2 - The following problem is addressed: given square matrices A and B, compute the smallest ε such that A + E and B + F have a common eigenvalue for some E, F with max(∥E∥, ∥F∥2) ≤ ε. An algorithm to compute this quantity to any prescribed accuracy is presented, assuming that eigenvalues can be computed exactly.

AB - The following problem is addressed: given square matrices A and B, compute the smallest ε such that A + E and B + F have a common eigenvalue for some E, F with max(∥E∥, ∥F∥2) ≤ ε. An algorithm to compute this quantity to any prescribed accuracy is presented, assuming that eigenvalues can be computed exactly.

KW - Eigenvalue perturbation

KW - Eigenvalue separation

KW - Pencil

KW - Pseudospectra

UR - http://www.scopus.com/inward/record.url?scp=34247362921&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34247362921&partnerID=8YFLogxK

U2 - 10.1137/050622584

DO - 10.1137/050622584

M3 - Article

VL - 28

SP - 348

EP - 359

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

SN - 0895-4798

IS - 2

ER -