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<p>Cyclic tridiagonal matrices, a specific subclass of quasi-tridiagonal matrices, frequently arise in theoretical and computational chemistry. This paper addresses the solution of cyclic tridiagonal linear systems with coefficient matrices that are subdiagonally dominant, superdiagonally dominant and weakly diagonally dominant. For the subdiagonally dominant case, we perform an elementary transformation to convert the matrix into a block 2-by-2 form, then solve the system using block <i>LU</i> factorization. For the superdiagonally dominant and weakly diagonally dominant cases, we extend this approach using block <i>LU</i> factorization and matrix similarity transformations. Our proposed algorithms outperform existing methods in terms of floating-point operations, memory storage, and data transmission. Numerical experiments, implemented in MATLAB, demonstrate the accuracy and efficiency of the proposed algorithms.</p>

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Fast and accurate recursive algorithms for solving cyclic tridiagonal linear systems

  • 期刊论文

  • 发表日期：

    2025年3月15日

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  • Su-Mei Li,
  • Xin Fan,
  • Yi-Fan Wang

摘要

Cyclic tridiagonal matrices, a specific subclass of quasi-tridiagonal matrices, frequently arise in theoretical and computational chemistry. This paper addresses the solution of cyclic tridiagonal linear systems with coefficient matrices that are subdiagonally dominant, superdiagonally dominant and weakly diagonally dominant. For the subdiagonally dominant case, we perform an elementary transformation to convert the matrix into a block 2-by-2 form, then solve the system using block LU factorization. For the superdiagonally dominant and weakly diagonally dominant cases, we extend this approach using block LU factorization and matrix similarity transformations. Our proposed algorithms outperform existing methods in terms of floating-point operations, memory storage, and data transmission. Numerical experiments, implemented in MATLAB, demonstrate the accuracy and efficiency of the proposed algorithms.