分块三对角方程组的数值解法  

A NUMERICAL ALGORITHM ON SOLVING BLOCK TRIDIAGONAL LINEAR SYSTEMS

作　　者：刘长河[1] 代西武[1] 汪元伦[2] 

机构地区：[1]北京建筑工程学院基础部,北京100044 [2]绵阳师范学院数学与信息科学系,四川绵阳621000

出　　处：《数值计算与计算机应用》2008年第1期39-48,共10页Journal on Numerical Methods and Computer Applications

摘　　要：本文给出一种求解分块三对角线性方程组的一种新算法.它是一种直接解法,可以避免迭代法所产生的误差积累.由于充分利用了分块三对角矩阵的特点,这又是一种快速解法.经过严格的理论证明可知,本文算法是数值稳定的.数值实验验证了本文的算法具有很高的精确度.In this paper, a kind of new algorithm on solving block tridiagonal linear systems is proposed. It is a direct scheme and can avoid accumulated error resulted by iterative methods. Our algorithm can solve block tridiagonal linear systems quickly because that the peculiarities of its coefficient matrix are fully utilized. It is strictly proved that our algorithm is stable. Value results have illustrated that our algorithm has high precision.

关 键 词：分块三对角矩阵 分块对角占优矩阵 线性方程组 数值解 误差分析 

分 类 号：O241.6[理学—计算数学] O241.81[理学—数学]