| 线性方程组的距离迭代解法 |
| |
| 引用本文： | 杨天标.线性方程组的距离迭代解法[J].德州学院学报,2012,28(2):26-29. |
| |
| 作者姓名： | 杨天标 |
| |
| 作者单位： | 长江师范学院数学与计算机学院,重庆涪陵,408100 |
| |
| 摘 要： | 目前,线性方程组的数值求解,常用的方法是Gauss-Seidel迭代法.Gauss-Seidel的收敛性要求条件很强.对于一般n元方程组,如果系数矩阵的秩小于n,则Gauss-Seidel迭代一般不能使用.本文所要介绍的距离迭代法,及其改进方法,折线迭代法,对于方程组基本上没有什么要求,只要有解,就一定能够得到.距离迭代法具有鲜明的几何意义,理论、方法十分朴素易懂,速度快,精度高,是一个值得推荐的优秀数值方法.
|
| 关 键 词： | Gauss-Seidel迭代 收敛性 单步定常迭代 距离迭代 折线迭代 |
Distance Iteration Method of Linear Equations |
| |
| YANG Tian-biao.Distance Iteration Method of Linear Equations[J].Journal of Dezhou University,2012,28(2):26-29. |
| |
| Authors: | YANG Tian-biao |
| |
| Institution: | YANG Tian-biao(College of Mathematics and Computer Science, Yangtze Normal University,Chongqing 408100,China) |
| |
| Abstract: | At present,frequently used numerical method in solving linear equations is Gauss-Seidel Iteration.To make this method converge,there are very strong restrictions.For a general n variable linear equation group,if the coefficient matrix has a smaller rank than n,the Gauss-Seidel method will often fail.This article introduces the so-called distance iteration.The method requires nothing of the equations,except that a solution must exist.Once it exists,then we can get it.Distance iteration has vivid geometrical significance,its theory and method are simple and easy to understand,the convergence is fast,and the precision is high.It is a remarkable and excellent numerical method. |
| |
| Keywords: | Gauss-Seidel Iteration Convergence One-Step Constant Iteration Distance Iteration Path Iteration |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
