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arXiv · 2006.15867

On the inversion of the block double-structured and of the triple-structured Toeplitz matrices and on the corresponding reflection coefficients

Inna Roitberg·Alexander Sakhnovich
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Abstract

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.

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Inna Roitberg, Alexander Sakhnovich. 2020-06-29. On the inversion of the block double-structured and of the triple-structured Toeplitz matrices and on the corresponding reflection coefficients. https://doi.org/10.1016/j.laa.2020.10.007

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