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On the Linear Convergence of a Covariance Factorization Algorithm

An algorithm for factoring a covariance function into its Hurwitz factors, which is based on the Cholesky factors of a certain matrix, was proposed by F.L. Bauer and others. This algorithm bears a close connection to the theory of orthogonal polynomials, and a closer one to the theory of prediction of stationary time series. In this paper these relations are pointed out and then used to advantage to prove the linear convergence of this algorithm.