Fast verification for all eigenpairs in symmetric positive definite generalized eigenvalue problems

Journal
Reliable Computing  
Volume
14
Start Page
24
End Page
45
Citation
Reliable Computing (14): 24-45 (2010-06-01)
Scopus ID
2-s2.0-79954514993
Publisher
[University of Louisiana at Lafayette]
A fast method for enclosing all eigenpairs in symmetric positive definite generalized eigenvalue problems is proposed. Firstly theorems on verifying all eigenvalues are presented. Next a theorem on verifying all eigenvectors is presented. The proposed method is developed based on these theorems. Numerical results are presented showing the efficiency of the proposed method. As an application of the proposed method, an efficient method of enclosing all eigenpairs in the quadratic eigenvalue problem is also sketched.
Subjects
Eigenpairs
Generalized eigenvalue problem
Numerical verification
DDC Class
004: Informatik
More Funding Information
This research was partially supported by Grant-in-Aid for Young Scientists (B) (19760055, 2007–2010) from the Ministry of Education, Science, Sports and Culture of Japan.