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A hybrid triangulation method for banded linear systems

Author

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  • Luo, Wei-Hua
  • Gu, Xian-Ming
  • Carpentieri, Bruno

Abstract

We propose a fast solution method for banded linear systems that transforms the original system into an equivalent one with an almost block triangular coefficient matrix, and then constructs a preconditioner based on this formulation. We analyze the algorithmic complexity of the new method and the eigenvalue distribution of the resulting preconditioned matrix. Numerical examples involving block tridiagonal, block Hessenberg and block pentadiagonal systems are illustrated to demonstrate the computational performance and the efficiency of the new matrix solver.

Suggested Citation

  • Luo, Wei-Hua & Gu, Xian-Ming & Carpentieri, Bruno, 2022. "A hybrid triangulation method for banded linear systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 97-108.
    • Handle: RePEc:eee:matcom:v:194:y:2022:i:c:p:97-108
    DOI: 10.1016/j.matcom.2021.11.012
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    References listed on IDEAS

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    1. Li, Hou-Biao & Huang, Ting-Zhu & Zhang, Yong & Liu, Xing-Ping & Li, Hong, 2009. "On some new approximate factorization methods for block tridiagonal matrices suitable for vector and parallel processors," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2135-2147.
    2. Luo, Wei-Hua & Huang, Ting-Zhu & Wu, Guo-Cheng & Gu, Xian-Ming, 2016. "Quadratic spline collocation method for the time fractional subdiffusion equation," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 252-265.
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