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 -