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.
翻译：通过BC-方法的动态变体解决逆向问题,基本上被缩减为倒转动态系统的连接操作员$C$T$,对此问题有说明。在数字上,人们需要倒转Gram矩阵$hat CäT ⁇ (CäT_i,f_j) ⁇ i,j=1N$,用于代表一组控制,$f_i。为了提高确定解决方案的准确性,人们必须增加金额N$,这导致计算量的迅速增加,特别是在多维情况下。然而,通过适当选择$f_j$,可以减少这一方法,因此,矩阵$\hat C ⁇ T$获得一个特定的块状托普利茨结构。在文件中,我们解释,该属性来自何处,并概述在BC-algoithms的数值执行中使用该属性的方法。
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