Spectral factorization and Nevanlinna-Schur algorithm in state space

A formulation for the Nevanlinna-Schur (NS) algorithm which operates on state-space realizations of matrix functions is presented. The state space form of the NS algorithm leads to a generalized version of the Chandrasekhar-type algorithm in linear optimal filtering. An NS-algorithm-based spectral factorization scheme with convergence estimates and error bounds is provided. The authors discuss how information on transmission zeros may be obtained and incorporated in the scheme to increase the rate of convergence. The proposed computationally efficient algorithm for solving the rational spectral factorization problem has a certain amount of flexibility which may be used to improve computational speed and numerical stability when compared with the Schur algorithm/discrete-time Riccati equation based approach