| 关于求解常微方程组的离散波形松驰方法的加速收敛 |
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| 引用本文： | 袁东锦.关于求解常微方程组的离散波形松驰方法的加速收敛[J].应用数学,2002,15(1):133-137. |
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| 作者姓名： | 袁东锦 |
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| 作者单位： | 扬州大学数学系,江苏,扬州,225002 |
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| 基金项目： | ThisworkissupportedbyReturnedOverseasStudentFoundationofJiangsuProvince(19982 317) . |
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| 摘 要： | 提出一种关于求解常微线性系统的离散波形松驰方法的新的加速收敛技巧。通过对系统矩阵A的分裂，该技巧使迭代矩阵（(zI M)^-1N）具有理想的较小谱半径。在LU分解的基础上给出了一个迭代算法以及用该法与Gauss-Seidel方不垢敛速进行比较的数值例子。
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| 关 键 词： | 常微分方程组 波形松驰 收敛性 分解 分裂 LU分解 迭代算法 |
| 文章编号： | 1001-9847(2002)01-0133-05 |
| 修稿时间： | 2001年6月25日 |
On the Accelerative Convergence of Discretized Waveform Method for Solving Ordinary Differential Systems |
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| YUAN Dong-jin.On the Accelerative Convergence of Discretized Waveform Method for Solving Ordinary Differential Systems[J].Mathematica Applicata,2002,15(1):133-137. |
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| Authors: | YUAN Dong-jin |
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| Abstract: | In this paper a new technique for acceler at ion of convergence of discretized waveform method is proposed for solving ordina ry linear differential systems. This technique is based on splitting the matrix A of the system in such a way that the resulting iteration matrix ((zI+M) -1N) has an ideally small spectral radius. An iterative algorithm is con structed based on the LU decomposition of the system matrix. Numerical resul t is reported to compare the convergence properties of this new method with thos e of the Gauss-Jacobi and the Gauss-Seidel method. |
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| Keywords: | Ordinary differential equations Waveform relaxation Con vergence Decomposition Splitting |
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