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Laplace方程五点差分格式的结构二次幂零矩阵迭代法
发表时间：2018-01-15 浏览量：2124 下载量：429
| 全部作者： | 张承平 |
| 作者单位： | 海南热带海洋学院海洋信息工程学院 |
| 摘 要： | 对于Laplace方程的五点差分格式，讨论奇数个点插入时形成的线性方程组，并对一系列不同的奇数个插入点的方程组，构造结构二次幂零矩阵迭代法。数值实验结果表明，结构二次幂零矩阵迭代法迭代次数比雅可比迭代法少，接近其一半次数，因而得出结构二次幂零矩阵迭代法比雅可比迭代法收敛速度快。同时与高斯赛德尔迭代法相比，结构二次幂零矩阵迭代法迭代次数略低。对于偶数个插入点所形成的线性方程组，取同样结构的结构二次幂零矩阵，其迭代次数比相近的奇数个插入点的迭代次数高。因此，在进行五点差分格式时应尽量采用插入奇数个点的方法。 |
| 关 键 词： | 计算数学；线性方程组；结构二次幂零矩阵；并行迭代法；Laplace方程；五点差分格式 |
| Title： | Structural 2-nilpotent matrix iterative method about the five points difference scheme of the Laplace equation |
| Author： | ZHANG Chengping |
| Organization： | School of Marine Information and Engineering, Hainan Tropical Ocean University |
| Abstract： | In this paper, according to the five point difference scheme for the Laplace equation, linear equations inserted odd points are formed and discussed. And for a series of equations of different inserted odd points, the structural 2-nilpotent matrices are structured in order to set up iterative methods. Numerical experiments show that the iterations of structural 2-nilpotent matrix iterative method are fewer than those of Jacobi iterative method, and almost closed to half of Jacobi iterative method. Thus it is concluded that the convergence rate of structural 2-nilpotent matrix iterative method is faster than that of Jacobi iterative method. The iterations of structural 2-nilpotent matrix iterative method are lower than those of Gauss-Seidel iterative method. Finally, the structural 2-nilpotent matrix of achieved linear equations after inserting even points is structured in the same way. The iterations of iterative method with inserting even points are higher than those with inserting similar structure of odd points. So the five point difference scheme inserted odd points is advocated. |
| Key words： | computational mathematics; linear equations; structural 2-nilpotent matrix; parallel iterative method; Laplace equation; five points difference scheme |
| 发表期数： | 2018年1月第1期 |
| 引用格式： | 张承平. Laplace方程五点差分格式的结构二次幂零矩阵迭代法[J]. 中国科技论文在线精品论文，2018，11（1）：11-16. |
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