带状矩阵线性代数方程组求解有效符号方法性能分析
Performance Analysis of Effective Symbolic Methods for Solving Band Matrix SLAEs
AI总结：
本文研究了三种符号算法在求解带状系数矩阵线性代数方程组时的性能，通过HPC平台进行实验，分析了算法稳定性及不同数据存储类别的表现。
摘要：
本文介绍了三种符号算法在求解具有七对角、五对角和三对角系数矩阵的带状矩阵线性代数方程组的实现性能研究。为了保证算法的稳定性，系数矩阵的唯一假设是非奇异。这些算法使用C++的GiNaC库和Python的SymPy库实现，考虑了五种不同的数据存储类别。通过高性能计算（HPC）平台“HybriLIT”和“Avitohol”进行性能分析。展示了实验设置以及在各个计算机系统上进行的计算结果和讨论。对这三个算法进行了分析。
英文摘要：
This paper presents an experimental performance study of implementations of three symbolic algorithms for solving band matrix systems of linear algebraic equations with heptadiagonal, pentadiagonal, and tridiagonal coefficient matrices. The only assumption on the coefficient matrix in order for the algorithms to be stable is nonsingularity. These algorithms are implemented using the GiNaC library of C++ and the SymPy library of Python, considering five different data storing classes. Performance analysis of the implementations is done using the high-performance computing (HPC) platforms "HybriLIT" and "Avitohol". The experimental setup and the results from the conducted computations on the individual computer systems are presented and discussed. An analysis of the three algorithms is performed.
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