Premium
A property of eigenvalue bounds for a class of symmetric tridiagonal interval matrices
Author(s) -
Yuan Quan,
Leng Huinan,
He Zhiqing
Publication year - 2011
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.753
Subject(s) - tridiagonal matrix , mathematics , eigenvalues and eigenvectors , interval (graph theory) , divide and conquer eigenvalue algorithm , class (philosophy) , matrix (chemical analysis) , upper and lower bounds , vertex (graph theory) , combinatorics , mathematical analysis , graph , computer science , physics , materials science , quantum mechanics , artificial intelligence , composite material
The eigenvalue bounds of interval matrices are often required in some mechanical and engineering fields. In this paper, we consider an interval eigenvalue problem with symmetric tridiagonal matrices. A theoretical result is obtained that under certain assumptions the upper and lower bounds of interval eigenvalues of the problem must be achieved just at some vertex matrices of the interval matrix. Then a sufficient condition is provided to guarantee the assumption to be satisfied. The conclusion is illustrated also by a numerical example. Copyright © 2010 John Wiley & Sons, Ltd.