Fast enclosure for all eigenvalues in generalized eigenvalue problems

Authors:
Shinya Miyajima
Affiliations:
Faculty of Engineering, Gifu University, 501-1193, Japan
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

A fast method for enclosing all eigenvalues in generalized eigenvalue problems Ax=@lBx is proposed. Firstly a theorem for enclosing all eigenvalues, which is applicable even if A is not Hermitian and/or B is not Hermitian positive definite, is presented. Next a theorem for accelerating the enclosure is presented. The proposed method is established based on these theorems. Numerical examples show the performance and property of the proposed method. As an application of the proposed method, an efficient method for enclosing all eigenvalues in polynomial eigenvalue problems is also sketched.