求解大型稀疏线代数方程组的一种迭代方法  

An Iterative Method for Solving Large Sparse Linear Algebraic Systems

作　　者：许波[1] 

机构地区：[1]江苏石油化工学院基础课部

出　　处：《江苏石油化工学院学报》1998年第2期35-37,共3页Journal of Jiangsu Institute of Petrochemical Technology

摘　　要：用迭法求解线性代数方程组时，由于收敛条件较严，只能对一些特殊矩阵（如对角占优、对称正定矩阵）构造迭代公式。而对于一般的线性代数方程组，尤其是大型稀疏方程组尚无一般的迭代公式。针对这一情况，介绍求解线性代数方程组的一种迭代方法。只要方程组存在唯一解，这种迭代方法便是无条件收敛的。还结合压缩存贮技术给出迭代公式，应用该方法可大大节省计算机内存，从而可在微机上求解大型稀疏线性代数方程组。算例表明这种方法收敛速度较快，稳定性较好，尤其对病态方程组十分有效。When the convergence iterative method is used to solve linear algebraic systems, its convergence condition is relatively strict. Therefore only some special matrixes such as diagonally dominant matrix, symmetry positive definite matrix, etc., can be solved with this method. And there is no convergence iterative method for solving general linear algebraic systems, especially large sparse linear algebraic systems. In view of this situation, the author introduces a different convergence iterative method in this thesis. If systems have the sole solution, this iterative method is unconditionally convergent. Furthermore, this thesis gives the iterative formula in the light of the technology of compressed memory, In this way the computer memory space may be saved to a large extent. Thus large sparse linear algebraic systems can be solved in a microcomputer. The examples in this paper show that the convergence of this method is quick and stable, and this iterative method is particularly suitable for solving morbid linear algebraic systems.

关 键 词：代数方程组 迭代 稀疏线 收敛速度 线性代数 

分 类 号：O241.6[理学—计算数学]