An iterative method for solving the spectral problem of complex symmetric matrices

An effective method for computing eigenvalues and eigenvectors of complex symmetric matrices in real arithmetic is proposed. The problem for computing eigenvalues and eigenvectors of complex symmetric matrices arises in chemical reactive problems. The problem of a complex matrix is equivalent to the spectral problem of a special 2 × 2 block real matrix. Our method uses similarity transformations and preserves the special block structure. The convergence theorem is proved. Numerical experiments are given.