A Variant of the Gohberg–Semencul Formula Involving Circulant Matrices
- 1 July 1991
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Matrix Analysis and Applications
- Vol. 12 (3) , 534-540
- https://doi.org/10.1137/0612038
Abstract
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.Keywords
This publication has 12 references indexed in Scilit:
- Displacement operator based decompositions of matrices using circulants or other group matricesLinear Algebra and its Applications, 1990
- Superfast Solution of Real Positive Definite Toeplitz SystemsSIAM Journal on Matrix Analysis and Applications, 1988
- The generalized Schur algorithm for the superfast solution of Toeplitz systemsPublished by Springer Nature ,1987
- Generalized Bezoutian and the inversion problem for block matrices, I. General schemeIntegral Equations and Operator Theory, 1986
- The split Levinson algorithmIEEE Transactions on Acoustics, Speech, and Signal Processing, 1986
- Implementation of "Split-radix" FFT algorithms for complex, real, and real-symmetric dataIEEE Transactions on Acoustics, Speech, and Signal Processing, 1986
- An efficient algorithm for a large Toeplitz set of linear equationsIEEE Transactions on Acoustics, Speech, and Signal Processing, 1979
- New inversion formulas for matrices classified in terms of their distance from Toeplitz matricesLinear Algebra and its Applications, 1979
- Displacement ranks of matrices and linear equationsJournal of Mathematical Analysis and Applications, 1979
- Inverses of Toeplitz Operators, Innovations, and Orthogonal PolynomialsSIAM Review, 1978