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

Publikationstyp
Journal Article
Publikationsdatum
2010-06-01
Sprache
English
Author
Miyajima, Shinya 
Ogita, Takeshi 
Rump, Siegfried M. orcid-logo
Oishi, Shin’ichi 
Institut
Zuverlässiges Rechnen E-19 
TORE-URI
http://hdl.handle.net/11420/8533
Enthalten in
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.
Schlagworte
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.