宁夏大学学报（自然科学版中英文）2026，Vol.47Issue(1)：1-13,13.DOI:10.20176/j.cnki.nxdz.20251215
一种基于对角矩阵分裂的快速迭代方法及其应用
A Kind of Fast Iterative Methods With the Application Based on Diagonal Matrix Splitting
摘要
Abstract
The fast solution of linear equations has always been one of the hot spots in scientific comput-ing.A kind of the diagonal matrix splitting iteration methods are provided,which is different from the classical matrix splitting methods.Taking the decomposition of the diagonal elements for coefficient matrix as the key point,some new preconditioners are constructed.Taking the tri-diagonal coefficient matrix as an example,the convergence domains and optimal relaxation factor of the new method are ana-lyzed theoretically.The presented new iteration methods are applied to solve linear algebraic equations,even 2D and 3D diffusion problems with the fully implicit discretization.The results of numerical experi-ments are matched with the theoretical analysis,and show that the iteration numbers are reduced greatly.The superiorities of presented iteration methods exceed some classical iteration methods dramatically.关键词
迭代/矩阵分裂/扩散方程/收敛性/最佳松弛因子Key words
iteration/matrix splitting/diffusion equation/convergence/optimal relaxation factor分类
数理科学引用本文复制引用
许秋燕..一种基于对角矩阵分裂的快速迭代方法及其应用[J].宁夏大学学报（自然科学版中英文）,2026,47(1):1-13,13.基金项目
The National Natural Science Foundations of China(12202219) （12202219）
the Natural Science Foundations of Ningxia(2024AAC02009,2023AAC05001) （2024AAC02009,2023AAC05001）
the Ningxia Youth Top Talents Training Project （）
