An explicit formula for the inverse of a pentadiagonal Toeplitz matrix

Chaojie Wang ^[1] ; Hongyi Li ^[1] ; Di Zhao ^[1]
1. [1] Beihang University
  
  Beihang University
  
  China
Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 278, Nº 1 (15 April 2015), 2015, págs. 12-18
Idioma: inglés
DOI: 10.1016/j.cam.2014.08.010
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Resumen
- In this paper, we mainly consider finding an explicit formula for the inverse of a pentadiagonal Toeplitz matrix. For that purpose, we first factorize the modified form of a pentadiagonal Toeplitz matrix by two tridiagonal Toeplitz matrices, and then use the Sherman–Morrison–Woodbury inversion formula. As a result, an explicit inverse of a pentadiagonal Toeplitz matrix is obtained under certain assumptions. And numerical experiments are given to show the effectiveness of our results.