On inverses of tridiagonal matrices

被引：1
|
作者：
Al-Hassan, Qassem M. [1 ]
机构：
[1] Univ Sharjah, Dept Basic Sci, Sharjah, U Arab Emirates
来源：
JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY | 2005年 / 8卷 / 01期
关键词：
Tridiagonal matrices; Crout's LU factorization; recurrence relation;
D O I：
10.1080/09720529.2005.10698020
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An algorithm for computing the inverse of a general tridiagonal matrix is introduced. This algorithm is obtained by factoring this matrix into the product of two bidiagonal matrices using Crout's LU factorization, one upper and one lower bidiagonal. A simple recurrence relation is used to generate a sequence of numbers, this sequence is then used to fill in the matrices L, u, L-1, u(-1) and consequently the required inverse.
引用
收藏
页码：49 / 58
页数：10
相关论文
共 50 条
  • [1] On the inverses of general tridiagonal matrices
    Li, Hou-Biao
    Huang, Ting-Zhu
    Liu, Xing-Ping
    Li, Hong
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 433 (05) : 965 - 983
  • [2] Characterization of the inverses of tridiagonal matrices
    Jing, Yan-Fei
    Huang, Ting-Zhu
    Advances in Matrix Theory and Applications, 2006, : 393 - 395
  • [3] Matrices Whose Inverses are Tridiagonal, Band or Block-Tridiagonal and Their Relationship with the Covariance Matrices of a Random Markov Process
    Brimkulov, Ulan
    FILOMAT, 2019, 33 (05) : 1335 - 1352
  • [4] Symbolic algorithms for the inverses of general k-tridiagonal matrices
    Jia, Jiteng
    Li, Sumei
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2015, 70 (12) : 3032 - 3042
  • [5] Two-sided bounds on the inverses of diagonally dominant tridiagonal matrices
    Nabben, R
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1999, 287 (1-3) : 289 - 305
  • [6] On computing the determinants and inverses of some special type of tridiagonal and constant-diagonals matrices
    Witula, Roman
    Slota, Damian
    APPLIED MATHEMATICS AND COMPUTATION, 2007, 189 (01) : 514 - 527
  • [7] A bidiagonalization-based numerical algorithm for computing the inverses of (p,q)-tridiagonal matrices
    Jia, Ji-Teng
    Xie, Rong
    Xu, Xiao-Yan
    Ni, Shuo
    Wang, Jie
    NUMERICAL ALGORITHMS, 2023, 93 (02) : 899 - 917
  • [8] A bidiagonalization-based numerical algorithm for computing the inverses of (p,q)-tridiagonal matrices
    Ji-Teng Jia
    Rong Xie
    Xiao-Yan Xu
    Shuo Ni
    Jie Wang
    Numerical Algorithms, 2023, 93 : 899 - 917
  • [9] Generalized Sherman–Morrison–Woodbury formula based algorithm for the inverses of opposite-bordered tridiagonal matrices
    Ji-Teng Jia
    Tomohiro Sogabe
    Journal of Mathematical Chemistry, 2020, 58 : 1466 - 1480
  • [10] Orthogonal rational functions and tridiagonal matrices
    Bultheel, A
    González-Vera, P
    Hendriksen, E
    Njåstad, O
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2003, 153 (1-2) : 89 - 97
12345