论文标题
在块双结构和三结构的Toeplitz矩阵以及相应反射系数的倒置上
On the inversion of the block double-structured and of the triple-structured Toeplitz matrices and on the corresponding reflection coefficients
论文作者
论文摘要
关于卷积操作员以及$ 1 $ -D（一维）情况的Toeplitz（和Block Toeplitz）矩阵的反转结果是经典的，并且有许多应用程序。去年，我们考虑了$ 2 $ -D的toeplitz-block toeplitz（TBT）矩阵的情况，描述了一个最小信息，这是恢复反矩阵的必要信息，并给出了反矩阵的完整表征。现在，我们开发了更复杂的块TBT矩阵和$ 3 $ -D toeplitz矩阵的方法。
The results on the inversion of convolution operators as well as Toeplitz (and block Toeplitz) matrices in the $1$-D (one-dimensional) case are classical and have numerous applications. Last year, we considered the $2$-D case of Toeplitz-block Toeplitz (TBT) matrices, described a minimal information, which is necessary to recover the inverse matrices, and gave a complete characterisation of the inverse matrices. Now, we develop our approach for the more complicated cases of block TBT-matrices and $3$-D Toeplitz matrices.
