Geodesic
Toeplitz matrices in the BC-method for the plane domains
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 51, Tome 506 (2021), pp. 21-35

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BC-method is an approach to inverse problems based on their relationship with boundary control theory and system theory. The main fragment of its numerical implementation is the inversion of the matrix of the so-called connecting operator. In multidimensional problems, the matrix is ill-conditioned and has a large size, which leads to a rapid growth in the number of operations needed for inverting. The paper reveals the block-Toeplitz structure of this matrix, using which it is possible to significantly reduce the amount of computations. 
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     author = {M. I. Belishev and N. A. Karazeeva},
     title = {Toeplitz matrices in the {BC-method} for the plane domains},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {21--35},
     publisher = {mathdoc},
     volume = {506},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_506_a3/}
}
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M. I. Belishev; N. A. Karazeeva. Toeplitz matrices in the BC-method for the plane domains. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 51, Tome 506 (2021), pp. 21-35. http://geodesic.mathdoc.fr/item/ZNSL_2021_506_a3/