  Solving inverse problems by dynamical variant of the BC-method is basically
reduced to inverting the connecting operator $C^T$ of the dynamical system, for
which the problem is stated. Realizing the method numerically, one needs to
invert the Gram matrix $\hat C^T=\{(C^Tf_i,f_j)\}_{i,j=1}^N$ for a
representative set of controls $f_i$. To raise the accuracy of determination of
the solution, one has to increase the size $N$, which, especially in the
multidimensional case, leads to a rapid increase in the amount of computations.
However, there is a way to reduce it by the proper choice of $f_j$, due to
which the matrix $\hat C^T$ gets a specific block-Toeplitz structure. In the
paper, we explain, where this property comes from, and outline a way to use it
in numerical implementation of the BC-algorithms.
