FAST DIAGONALIZATION OF LARGE AND DENSE COMPLEX SYMMETRICAL MATRICES,WITH APPLICATIONS TO QUANTUM REACTION DYNAMICS

We present a new fast and efficient algorithm for computing the eigenv alues and eigenvectors of large-size nondefective complex symmetric ma trices. Our work was motivated by of this problem in recent methods fo r solving chemical reactive problems. The algorithm we present is simi liar to the QR (QL) algorithm for complex Hermitian matrices, but we u se complex orthogonal (not unitary) transformations. The new algorithm is faster by an order of magnitude than the corresponding EISPACK rou tine, and is also more amenable for modern parallel and vector superco mputers. We further present improved perturbation bounds for the House holder transformation, which lies at the basis of the whole transforma tion.