摘要：线性方程组的数值求解常见于许多科学与工程计算领域.本文研究了求解大型线性方程组的主要迭代算法，对一些迭代法进行了详细的讨论，并从理论上对收敛性进行分析. 

　　微分方程是表达自然规律的一种自然的数学语言.它从生产实践与科学技术中产生，而又成为现代科学技术中分析问题与解决问题的一个强有力的工具.人们在探求物质世界某些规律的过程中，一般很难完全依靠实验观测认识到该规律，反而是依照某种规律存在的联系常常容易被我们捕捉到，而这种规律用数学语言表达出来，其结果往往形成一个微分方程，而一旦求出方程的解，其规律则一目了然.所以我们必须能够求出它的解.

关键词：平面方程； 线性方程组； 微分方程

Abstract： Numerical methods for linear systems are very important in many areas. Several iterative methods for solving the large linear systems are presented. Same iterative methods are discussed from the iterative formulas and convergence.

　　　Differential expression of natural law is a natural mathematical language. It from the production practice and science and technology generation but modern science and technology in analyzing and solving problems in a powerful tool. Some people in the law to explore the process of the material world, the general experimental observation is difficult to completely rely on recognizing that the law, but there is a link in accordance with certain laws are often easy to catch us, and such laws expressed in mathematical language, which often results in the formation of a differential equation, and once obtained equation, the law is clear. So we must be able to find its solution.

key words：plane equation, linear equations, differential equations