Numerical enclosure for each eigenvalue in generalized eigenvalue problem

Authors:
Shinya Miyajima
Affiliations:
-
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

Citing 6
Cited 0

Guaranteed inclusions for the complex generalized eigenproblem

Computing
Large-scale complex eigenvalue problems

Journal of Computational Physics
The calculation of guaranteed bounds for eigenvalues using complementary variational principles

Computing
The symmetric eigenvalue problem

The symmetric eigenvalue problem
Matrix analysis and applied linear algebra

Matrix analysis and applied linear algebra
Fast enclosure for all eigenvalues in generalized eigenvalue problems

Journal of Computational and Applied Mathematics

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Abstract

An algorithm for enclosing all eigenvalues in generalized eigenvalue problem Ax=@lBx is proposed. This algorithm is applicable even if A@?C^n^x^n is not Hermitian and/or B@?C^n^x^n is not Hermitian positive definite, and supplies nerror bounds while the algorithm previously developed by the author supplies a single error bound. It is proved that the error bounds obtained by the proposed algorithm are equal or smaller than that by the previous algorithm. Computational cost for the proposed algorithm is similar to that for the previous algorithm. Numerical results show the property of the proposed algorithm.