雅可比迭代法与高斯-塞德尔迭代法研究

Analysis on the Jacobi and Gauss-Seidel Iterative Method

在求解大型线性方程组时,雅克比迭代法与高斯-塞德尔迭代法相对于直接法而言,具有保持迭代矩阵不变的特点,计算程序一般比较简单,且对于许多问题收敛速度比较快。通过求解物理模型中的两点边值问题得到一些数值来比较两种迭代法的迭代效果,验证一些已有的结论,并用所设计的程序来求解一些实际问题。

Jacobi iterative method and Gauss - Seidel iterative method compared to the direct methods keep iteralive matrix unchanged for solving large linear systems, the programs are relatively simple and have faster convergence rate for many problems. This paper throung the solutions of two-point boundary value problem in physical models based on the two iterative methods compares their iterative effection, confirms the existent conclusions and uses the algorithm to solve some practical problems.