Fast Diagonalization of Large and Dense Complex Symmetric Matrices, with Applications to Quantum Reaction Dynamics

We present a new fast and efficient algorithm for computing the eigenvalues and eigenvectors of large-size nondefective complex symmetric matrices. Our work was motivated by the emergence of this problem in recent methods for solving chemical reactive problems. The algorithm we present is similiar to the QR (QL) algorithm for complex Hermitian matrices, but we use complex orthogonal (not unitary) transformations. The new algorithm is faster by an order of magnitude than the corresponding EISPACK routine, and is also more amenable for modern parallel and vector supercomputers. We further present improved perturbation bounds for the Householder transformation, which lies at the basis of the whole transformation.