Fast and accurate recursive algorithms for solving cyclic tridiagonal linear systems

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2025-03-15 DOI:10.1007/s10910-025-01716-x

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

引用次数: 0

Abstract

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.

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求解循环三对角线性系统的快速精确递归算法

循环三对角矩阵是拟三对角矩阵的一个特殊子类，在理论化学和计算化学中经常出现。研究了具有次对角占优、超对角占优和弱对角占优系数矩阵的循环三对角线性系统的解。对于次对角占优的情况，我们通过初等变换将矩阵转化为2 × 2的块形式，然后用块LU分解求解系统。对于超对角占优和弱对角占优的情况，我们使用块LU分解和矩阵相似变换扩展了该方法。我们提出的算法在浮点运算、内存存储和数据传输方面优于现有方法。在MATLAB中进行的数值实验验证了所提算法的准确性和有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematical Chemistry 化学-化学综合

CiteScore

3.70

自引率

17.60%

发文量

105

审稿时长

6 months

期刊介绍： The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches. Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.