On asymptotic accuracy in $L_1$ of a dynamical algorithm for reconstructing a disturbance

In the paper, a modification of the dynamical algorithm by Yu. S. Osipov and A. V. Kryazhimskii is suggested. This modification possesses in the space $L_1$ an asymptotic order of accuracy arbitrarily close to 1/2. A possibility to attain this order in the class of finite-step dynamical algorithms is considered.