Geodesic
On certain decompositions of complex inverse Toeplitz matrices and related fast algorithms for solving linear systems with Toeplitz coefficient matrices
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 8, pp. 1227-1232 
V. I. Gel'fgat. On certain decompositions of complex inverse Toeplitz matrices and related fast algorithms for solving linear systems with Toeplitz coefficient matrices. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 8, pp. 1227-1232. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_8_a0/
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     title = {On certain decompositions of complex inverse {Toeplitz} matrices and related fast algorithms for solving linear systems with {Toeplitz} coefficient matrices},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Formulas for inverting nonsingular Toeplitz matrices with complex entries are derived. These formulas either refine known ones or are new. They make it possible to develop economical algorithms for calculating products of inverse Toeplitz matrices with vectors.

[1] Voevodin V. V., Tyrtyshnikov E. E., Vychislitelnye protsessy s teplitsevymi matritsami, Nauka, M., 1987 | MR | Zbl

[2] Yaroslavskii L. P., “Sdvinutye diskretnye preobrazovaniya Fure”, Problemy peredachi informatsii, XV:4 (1979), 102–105 | MR

[3] Nussbaumer G., Bystroe preobrazovanie Fure i algoritmy vychisleniya svertok, Radio i svyaz, M., 1985 | MR | Zbl

[4] Gelfgat V. I., “Usloviya kommutirovaniya teplitsevykh matrits”, Zh. vychisl. matem. i matem. fiz., 38:1 (1998), 11–14 | MR