A note on inversion of Toeplitz matrices
โ Scribed by Xiao-Guang Lv; Ting-Zhu Huang
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 157 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
โฆ Synopsis
It is shown that the invertibility of a Toeplitz matrix can be determined through the solvability of two standard equations. The inverse matrix can be denoted as a sum of products of circulant matrices and upper triangular Toeplitz matrices. The stability of the inversion formula for a Toeplitz matrix is also considered.
๐ SIMILAR VOLUMES
In this paper we show that the group inverse of a real singular Toeplitz matrix can be represented as the sum of products of lower and upper triangular Toeplitz matrices. Such a matrix representation generalizes "Gohberg-Semencul formula" in the literature.
We consider the asymptotic behaviour of the smallest singular values of the n x N sections of a general infinite Cauchy-Toeplitz matrix.