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A symbolic algorithm for periodic tridiagonal systems of equations

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Abstract

In the current paper, we present a novel symbolic algorithm for solving periodic tridiagonal linear systems without imposing any restrictive conditions. The computational cost of the algorithm is less than or almost equal to those of three well-known algorithms given by Chawla and Khazal (Int. J. Comput. Math. 79(4):473–484, 2002) and by El-Mikkawy (Appl. Math. Comput. 161:691–696, 2005), respectively. In addition, the solution of periodic anti-tridiagonal linear systems is also discussed. Two numerical experiments are provided in order to illustrate the performance and effectiveness of our algorithm. All of the experiments were performed on a computer with aid of programs written in MATLAB.

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Acknowledgments

This work was supported by the Natural Science Foundation of China (NSFC) under Grant 11371287 and the International Science and Technology Cooperation Program of China under Grant 2010DFA14700.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an , 710049, Shaanxi, China

    Ji-Teng Jia

  2. Department of Building Environment and Services Engineering, Xi’an Jiaotong University, Xi’an , 710049, Shaanxi, China

    Qiong-Xiang Kong

Authors
  1. Ji-Teng Jia
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  2. Qiong-Xiang Kong
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Correspondence to Ji-Teng Jia.

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Jia, JT., Kong, QX. A symbolic algorithm for periodic tridiagonal systems of equations. J Math Chem 52, 2222–2233 (2014). https://doi.org/10.1007/s10910-014-0378-1

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  • DOI: https://doi.org/10.1007/s10910-014-0378-1

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