A generalized symbolic Thomas algorithm for the solution of opposite-bordered tridiagonal linear systems

Jiteng Jia ^[1] ; Tomohiro Sogabe ^[2] ; Sumei Li ^[1]
1. [1] Xi'an Jiaotong University
  
  Xi'an Jiaotong University
  
  China
2. [2] Aichi Prefectural University
  
  Aichi Prefectural University
  
  Naka-ku, Japón
Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 290, Nº 1, 2015, págs. 423-432
Idioma: inglés
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Resumen
- In the current paper, we present a generalized symbolic Thomas algorithm, that never suffers from breakdown, for solving the opposite-bordered tridiagonal (OBT) linear systems. The algorithm uses a fill-in matrix factorization and can solve an OBT linear system in O(n)O(n) operations. Meanwhile, an efficient method of evaluating the determinant of an opposite-bordered tridiagonal matrix is derived. The computational costs of the proposed algorithms are also discussed. Moreover, three numerical examples are provided in order to demonstrate the performance and effectiveness of our algorithms and their competitiveness with some already existing algorithms. All of the experiments are performed on a computer with the aid of programs written in Matlab.