Numerical Methods for Simultaneous Diagonalization

A Jacobi-like algorithm for simultaneous diagonalization of commuting pairs of complex normal matrices by unitary similarity transformations is presented. The algorithm uses a sequence of similarity transformations by elementary complex rotations to drive the off-diagonal entries to zero. Its asymptotic convergence rate is shown to be quadratic and numerically stable. It preserves the special structure of real matrices, quaternion matrices, and real symmetric matrices.