Numerical enclosure for each eigenvalue in generalized eigenvalue problem

An algorithm for enclosing all eigenvalues in generalized eigenvalue problem Ax=λBxAx=λBx is proposed. This algorithm is applicable even if A∈Cn×nA∈Cn×n is not Hermitian and/or B∈Cn×nB∈Cn×n is not Hermitian positive definite, and supplies nnerror 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.