中北大学学报（自然科学版）2025，Vol.46Issue(5)：661-666,6.DOI:10.62756/jnuc.issn.1673-3193.2023.07.0004
求解大型稀疏矩阵方程组的SPIKE算法
The SPIKE Algorithm for Solving Large Sparse Matrix Equations
摘要
Abstract
A recursive SPIKE algorithm was presented based on DS matrix decomposition,which was very different from LU decomposition algorithm and QR decomposition algorithm.The SPIKE algorithm used a novel decomposition method to balance communication overhead with arithmetic cost to achieve bet-ter scalability than other methods on modern parallel architectures.Firstly,the basic operating principle of a recursive SPIKE algorithm was introduced by four aspects:partitioning coefficient matrix,DS decompo-sition,extraction and solution of simplified coefficient matrix equations.The SPIKE algorithm was applied to specific linear equations with different coefficient matrix for the first time.Three sets of numeri-cal experiments gave the results and running time of each solution algorithm.The experimental results show that the recursive SPIKE algorithm can not only obtain accurate results,but also has a faster solu-tion speed.Experiments indicate the computing time of the proposed algorithms is about 40 percent of LU decomposition algorithm,and about 8 percent of QR decomposition algorithm.关键词
一般带状矩阵/三对角矩阵/DS矩阵分解/递归SPIKE算法Key words
general banded matrix/tridiagonal matrix/DS matrix decomposition/recursive SPIKE algorithm分类
数理科学引用本文复制引用
秦芳芳,左沐雨,季一木..求解大型稀疏矩阵方程组的SPIKE算法[J].中北大学学报（自然科学版）,2025,46(5):661-666,6.基金项目
国家自然科学基金资助项目(11801281) （11801281）
江苏省博士后科研资助项目(2020Z380) （2020Z380）
