大规模带状线性方程组的追赶法  

A Forward Elimination and Backward Substitution Algorithm for Large-scale Banded Linear Systems

作　　者：王礼广[1] 谭林[1] 罗迪凡[1] 杨晓霖[1] 谭良[1] 

机构地区：[1]南华大学数理学院,湖南衡阳421001

出　　处：《南华大学学报（自然科学版）》2011年第4期70-74,共5页Journal of University of South China：Science and Technology

基　　金：国家自然科学基金资助项目(60773022);南华大学博士科研启动基金资助项目(2010XQD12)

摘　　要：利用五对角线性方程组的追赶法思想矩阵LU分解的方法,推导出任意带宽的大规模带状线性方程组的追赶法.理论推导表明:对于带宽为2t+1的n阶带状线性方程组,该算法的运算量级为O([2t2+5t+3]n),存储量级为O[2(t+1)n].数值实验表明:该算法比其他一些算法有明显的速度和内存优势.这极大地提高了解线性方程的速度.Derives a forward elimination and backward substitution algorithm for lage-scale banded linear systems with any bandwidth,using ones with quinary diagonal linear systems.It is deduced theoretically that the operational level is O（[2t2＋5t＋3]n） and the storage level is O[2（t＋1）n] for a banded linear system with bandwidth 2t＋1 and order n.It is shown that in the numerical experiments this algorithm has some advantages in computational cost and need memory evidently,compared to others.It improves largely the rate of computing for solving linear systems.

关 键 词：带状矩阵 稀疏矩阵 线性方程组 

分 类 号：O241.82[理学—计算数学]