三对角方程组通用性迭代解法  

General Iteration Algorithm to Solve a Tridiagonal Equations

作　　者：李安志[1] 任继念[1] 崔蔚[1] 

机构地区：[1]中国工程物理研究院工学院,四川绵阳621900

出　　处：《四川师范大学学报（自然科学版）》2013年第1期57-60,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(10802081)资助项目

摘　　要：在文献(四川师范大学学报:自然科学版,2008,31(2):187-188.)的基础上,提出一种对任意相容性三对角方程组均有效的迭代算法,证明该算法的收敛性,并设计并行处理方案和测试用例.该算法基本思想是:利用三对角方程组系数矩阵中行向量的部分正交性,将三对角方程组系数矩阵分为3组,使组内行向量相互正交,通过压缩存储将3组行向量压缩为3个行向量,从第一组开始用文献的方法在3组之间循环迭代,并取加速因子为1.该算法的特点是:对任意相容性三对角方程组均收敛,易于并行且节省存储空间,特别适合大型和超大型方程组的求解.An effective iterative algorithm to solve a tridiagonal equations of arbitrary compatibility is proposed based on reference （J. Sichuan Normal Univ. ：Natural Sci. ,2008,31 （2） ：187-188. ）. The convergence of the algorithm is proved, and a parallel processing scheme and test cases are designed. The basic idea of this algorithm is as follows. Firstly, the coefficient matrix of a tridiagonal equation is divided into three groups such that all the row vectors in the same group are mutually orthogonal. Secondly, by compressing storage, the row vectors in the three groups are compressed into three row vectors. And finally, starting from the first group, the itera- tion is recycled among the three groups with the accelerated factor 1. The algorithm is convergent for any tridiagonal equation with arbi- trary compatibility and is easily carried out parallel. Moreover, the algorithm can save storage space and especially suitable for solving large-scale and super-large tridiagonal equations.

关 键 词：三对角方程组 相容性 并行迭代算法 加速因子 

分 类 号：O241.6[理学—计算数学]