A Variant of the Gohberg–Semencul Formula Involving Circulant Matrices
Gregory S. Ammar, Paul Gader · SIAM Journal on Matrix Analysis and Applications · 1991
The Gohberg–Semencul formula expresses the inverse of a Toeplitz matrix as the difference of products of lower triangular and upper triangular Toeplitz matrices. In this paper the idea of cyclic displacement structure is used to show that the upper triangular matrices in this formula can be replaced by circulant matrices. The resulting computational savings afforded by this modified formula is discussed.