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Numerical enclosure for each eigenvalue in generalized eigenvalue problem
Authors:Shinya Miyajima
Institution:
  • Faculty of Engineering, Gifu University, 501-1193, Japan
  • Abstract:An algorithm for enclosing all eigenvalues in generalized eigenvalue problem Ax=λBx is proposed. This algorithm is applicable even if ACn×n is not Hermitian and/or BCn×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.
    Keywords:65F15  65G20  65G50
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