The interval eigenvalue problem: (Review article)

Mohamed A. Shalaby*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

The interval eigenvalue problem AI 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 languageEnglish (US)
Title of host publicationEuropean Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000
StatePublished - 2000
Externally publishedYes
EventEuropean Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000 - Barcelona, Spain
Duration: Sep 11 2000Sep 14 2000

Other

OtherEuropean Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000
CountrySpain
CityBarcelona
Period09/11/0009/14/00

Keywords

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

ASJC Scopus subject areas

  • Artificial Intelligence
  • Applied Mathematics

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