Efficient solution of Lyapunov equation for matrix autoregressive models and its application to the inverse Levinson problem

A novel efficient method for solving the discrete Lyapunov equation is presented, for the case where a matrix autoregressive model is assumed. This leads to an efficient procedure for solving the inverse Levinson problem, namely - constructing ladder realizations for given AR models (rather than for given covariance sequences). The method is based on a recently described method of inverting matrices that are sums of block-Toeplitz and block-Hankel matrices. The procedure is then shown to yield a stability test for the given autoregressive model.