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结构二次幂零矩阵迭代法的并行计算
发表时间：2018-04-13 浏览量：1586 下载量：205
| 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： | 针对Laplace方程五点差分格式插入69个点得到的线性方程组，将其进行标准化处理，构造结构二次幂零矩阵迭代法。采用Matlab软件，通过 CPU 编程以及调用GPU并行工具箱编程对比，同时与高斯赛德尔迭代法进行对比。数值实验表明，结构二次幂零矩阵迭代法CPU计算耗时达到GPU计算耗时的14倍以上，而高斯赛德尔迭代法CPU耗时达到结构二次幂零矩阵迭代法CPU计算耗时的2倍以上，说明结构二次幂零矩阵迭代法具有良好的并行性，非常适合大规模的并行编程，尤其采用GPU进行计算能节省大量时间，非常适合GPU并行编程计算。 |
| 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： | Parallel computation of iterative methods on structural 2-nilpotent matrices |
| Author： | ZHANG Chengping |
| Organization： | School of Marine Information and Engineering, Hainan Tropical Ocean College |
| Abstract： | In this paper, the linear equations Laplace equation of the five point difference scheme inserted into the 69 points are normalized. And the structural 2-nilpotent matrices are structured using Matlab software with CPU programming and calling parallel GPU toolbox. The structural 2-nilpotent matrices iterative method is compared with Gauss Seidel iterative method. Mathematical experiment shows that the computing time of the structural 2-nilpotent matrices iterative method by CPU is 14 times more than that by GPU. And the computing time of the Gauss-Seidel iterative method by CPU is 2 times more than that of the structural 2-nilpotent matrices iterative method by CPU. It shows that the structural 2-nilpotent matrices iterative method has good parallelism and is very suitable for parallel programming in large scale, especially combined with GPU, the method can save a lot of time. So the method is very suitable for GPU parallel programming computation. |
| 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4月第7期 |
| 引用格式： | 张承平. 结构二次幂零矩阵迭代法的并行计算[J]. 中国科技论文在线精品论文，2018，11（7）：698-704. |
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