Numerical enclosure for each eigenvalue in generalized eigenvalue problem

An algorithm for enclosing all eigenvalues in generalized eigenvalue problem Ax = lambda Bx is proposed. This algorithm is applicable even if A is an element of C-nxn is not Hermitian and/or B is an element of C-nxn is not Hermitian positive definite, and supplies n error 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. (C) 2011 Elsevier By. All rights reserved.