| 异步并行非线性对称Gauss-Seidel迭代算法 |
| |
| 引用本文： | 白中治.异步并行非线性对称Gauss-Seidel迭代算法[J].计算数学,1998,20(2):187-200. |
| |
| 作者姓名： | 白中治 |
| |
| 作者单位： | 中国科学院计算数学与科学工程计算研究所科学与工程计算国家重点实验室 |
| |
| 基金项目： | 国家自然科学基金!19601036 |
| |
| 摘 要： | 1．引言考虑非线性方程组其中A＝（a。。）EL（＊”）为＊一矩阵，B＝（衬。）EL（＊”）为非负矩阵，呐X）一（p。（X。》，4（二）＝（吵k（kk》：＊一＊一为连续的对角映射，而6＝（6k）E＊一为已知向量．这里，什小：”一”均可微，但二者的导函数并不一定连续．这类方程组具有丰富的实际背景．例如，描述冰体溶解过程的著名的Stefan问题，就可归结为问题（1·1）的数值求解（见［l］）．为在多处理机系统上有效地求解问题（1．1），文山利用这类非线性方程组的特殊结构，建立了一类并行非线性Gauss—Seidel型迭代算法．为避免该算…
|
| 关 键 词： | 非线性方程组 G－S算不地 异步迭代 全局收敛性 |
ASYNCHRONOUS PARALLEL NONLINEAR SYMMETRIC GAUSS-SEIDEL ITERATION METHODS |
| |
| Bai Zhong-zhi.ASYNCHRONOUS PARALLEL NONLINEAR SYMMETRIC GAUSS-SEIDEL ITERATION METHODS[J].Mathematica Numerica Sinica,1998,20(2):187-200. |
| |
| Authors: | Bai Zhong-zhi |
| |
| Institution: | Bai Zhong-zhi (State Key Laboratory of Scientific/Engineering Computing,Institute of Computational Mathematics and Scientific/Engineering Computing,Chinese Academy of Sciences, Beijing) |
| |
| Abstract: | Asynchronous parallel multisplitting nonlinear symmetric Gauss-Seidel methods are established for the system of nonlinear equations , withA, B∈L(Rn) being matrices of particular properties, being diagonal and continuous mappings, and b ∈Rn a known vector. The establishments of these new methods are according to the principle of sufficiently using the delayed information and are concerning about the concrete characteristics of the multiprocessor systems. Therefore, they have considerably higher parallel computingefficiency. The global convergenge as well as the asymptotic convergence rates of these new methods are investigated in detail under suitable conditions. |
| |
| Keywords: | System of nonlinear equations Matrix multisplitting Gauss-Seidel method Asynchronous iteration Global convergence Asymptotic convergence rate |
| 本文献已被 CNKI 维普 等数据库收录！ |
| 点击此处可从《计算数学》浏览原始摘要信息 |
| 点击此处可从《计算数学》下载免费的PDF全文 |
