TY - GEN

T1 - The interval eigenvalue problem

T2 - European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000

AU - Shalaby, Mohamed A.

PY - 2000

Y1 - 2000

N2 - 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).

AB - 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).

KW - Eigenvalue bounds (65G99).

KW - Eigenvalues and eigenvectors (65 F15)

KW - Interval arithmetics (65G10)

KW - Linear interval equations (65F10)

UR - http://www.scopus.com/inward/record.url?scp=84893344778&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84893344778

SN - 8489925704

SN - 9788489925700

T3 - European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000

BT - European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000

Y2 - 11 September 2000 through 14 September 2000

ER -