A generalized symbolic Thomas algorithm for the solution of opposite-bordered tridiagonal linear systems
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Jiteng Jia [1] ; Tomohiro Sogabe [2] ; Sumei Li [1]
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[1] Xi'an Jiaotong University
Xi'an Jiaotong University
China
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[2] Aichi Prefectural University
Aichi Prefectural University
Naka-ku, Japón
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- Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 290, Nº 1, 2015, págs. 423-432
- Idioma: inglés
- DOI: 10.1016/j.cam.2015.05.026
- Enlaces
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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.
