## Abstract

The interval eigenvalue problem A^{I} x = λx is discussed with an extensive survey to methods of solution available in the literature. The solution of such a problem is to apply the techniques of interval analysis on interval matrices to answer three main questions:(i)What are the location of the eigenvalues of an interval matrix?, (ii) How does the spectrum of an interval matrix depend on the spectrum of its end matrices? And (iii) how to compute the exact lower and upper bounds for every eigenpair of an interval matrix?. The stability of interval matrices is also defined, presented, and reviewed. Some applications and related topics are also presented. These applications are: Pole Assignment Problem (PAP), Telerance Analysis Problem (TAP), atomic physics, structural analysis, vibrations and robotics. The related topics are: enclosures of eigenpairs, Singular Value Decomposition (SVD), programming languages and applications on interval computation (optimzation, identification parallelism and linear porgramming).

Original language | English (US) |
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Title of host publication | European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000 |

State | Published - 2000 |

Externally published | Yes |

Event | European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000 - Barcelona, Spain Duration: Sep 11 2000 → Sep 14 2000 |

### Other

Other | European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000 |
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Country | Spain |

City | Barcelona |

Period | 09/11/00 → 09/14/00 |

## Keywords

- Eigenvalue bounds (65G99).
- Eigenvalues and eigenvectors (65 F15)
- Interval arithmetics (65G10)
- Linear interval equations (65F10)

## ASJC Scopus subject areas

- Artificial Intelligence
- Applied Mathematics