Spectral factorization by symmetric extraction for a vibrating string with low damping

One considers the method of spectral factorization, (J. Winkin et al., 2002; F.M. Callier et al., 1992; F.M. Callier et al., 1990), for a scalar coercive spectral density in the framework of the Callier-Desoer algebra of distributed parameter system transfer functions and the context of LQ-optimal control. This method is applied to a vibrating string with low damping. The latter is reported to satisfy the convergence criteria of the method, which are known to hold for a class of semigroup Hubert state-space systems with a Riesz-spectral generator. Moreover numerical results are given and commented with respect to the observed slow speed of convergence.