Jacobi和Gauss-Seidel迭代法求解线性方程组的分析及应用 |
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引用本文: | 杜衡吉,徐昆良.Jacobi和Gauss-Seidel迭代法求解线性方程组的分析及应用[J].曲靖师专学报,2011(3):46-50. |
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作者姓名: | 杜衡吉 徐昆良 |
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作者单位: | 曲靖师范学院计算机科学与工程学院,云南曲靖655011 |
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基金项目: | 云南省教育厅科学研究基金项目“数值计算方法教学改革与实践”(08C0181) |
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摘 要: | 先描述了Jacob i和Gauss-Se idel迭代法求解线性方程组的基本思想,然后给出三个收敛定理并分别对它们作出解释,举例进行分析和比较,最后给出算法,并用程序求解算例,对迭代法的学习和应用有着十分重要的意义.
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关 键 词: | Jacobi迭代法 Gauss-seidel迭代法 谱半径 对角占优阵 |
Analysis of Linear Systems through Jacobi and Gauss-Seidel Iteration Its Application |
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Authors: | Du Hengji Xu Kunliang |
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Institution: | (School of Computer Science and Computer Engineering,Qujing Normal University,Qujing Yunnan 655011,P.R.China) |
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Abstract: | The basic idea of Jacobi and Gauss-Seidel iteration method for solving the ??linear equations is discussed.Then three Convergence theorem are obtained,explained,analyzed and compared with examples and the algorithm is obtained. |
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Keywords: | Gauss-Seidel iteration Jacobi iteration Spectral radius Diagonally dominant matrices |
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