An explicit formula for the inverse of a pentadiagonal Toeplitz matrix

被引：18

作者：

Wang, Chaojie ^{[1
]}

Li, Hongyi ^{[1
]}

Zhao, Di ^{[1
]}

机构：

[1] Beihang Univ, Sch Math & Syst Sci, LMIB, Beijing 100191, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2015年 / 278卷

基金：

中国国家自然科学基金;

关键词：

Inverse; Pentadiagonal matrix; Toeplitz matrix; Factorization; Sherman-Morrison-Woodbury inversion; BOUNDARY-VALUE METHODS; NUMERICAL RECIPES; EQUATION;

D O I：

10.1016/j.cam.2014.08.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：12 / 18

页数：7

共 50 条

[41] A note on computing the inverse of a triangular Toeplitz matrix
Belhaj, Skander
Dridi, Marwa
APPLIED MATHEMATICS AND COMPUTATION, 2014, 236 : 512 - 523
[42] Asymptotic inverse of the Toeplitz matrix and Green kernel
Rambour, P
Rinkel, JM
Seghier, A
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2000, 331 (11): : 857 - 860
[43] A bound for the inverse of a lower triangular Toeplitz matrix
Vecchio, A
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2003, 24 (04) : 1167 - 1174
[44] Explicit inverse of symmetric, tridiagonal near Toeplitz matrices with strictly diagonally dominant Toeplitz part
Kurmanbek, Bakytzhan
Erlangga, Yogi
Amanbek, Yerlan
SPECIAL MATRICES, 2025, 13 (01):
[45] Explicit inverse of a generalized Vandermonde matrix
Ei-Mikkawy, MEA
APPLIED MATHEMATICS AND COMPUTATION, 2003, 146 (2-3) : 643 - 651
[46] AN EXPLICIT ESTIMATE ON NORM OF INVERSE OF A MATRIX
FREEDMAN, HI
SIAM REVIEW, 1969, 11 (02) : 254 - &
[47] ON THE EXPLICIT INVERSE AND CONDITIONING OF A TRIDIAGONAL MATRIX
USMANI, RA
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 1992, 41 (3-4) : 201 - 213
[48] An elementary algorithm for computing the determinant of pentadiagonal Toeplitz matrices
Cinkir, Zubeyir
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2012, 236 (09) : 2298 - 2305
[49] An eigenvalue localization theorem for pentadiagonal symmetric Toeplitz matrices
Elouafi, Mohamed
LINEAR ALGEBRA AND ITS APPLICATIONS, 2011, 435 (11) : 2986 - 2998
[50] An Explicit Formula for the Inverse of Arrowhead and Doubly Arrow Matrices
Salkuyeh D.K.
Beik F.P.A.
International Journal of Applied and Computational Mathematics, 2018, 4 (3)

← 1 2 3 4 5 →