| 求解循环三对角方程组的追赶法 |
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| 引用本文： | 李文强,马民. 求解循环三对角方程组的追赶法[J]. 科技导报(北京), 2009, 27(14): 69-72 |
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| 作者姓名： | 李文强 马民 |
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| 作者单位： | 河南师范大学数学与信息科学学院,河南新乡,453007 |
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| 基金项目： | 河南师范大学青年基金 |
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| 摘 要： | 利用LU分解的思想,首先将循环三对角方程组的系数矩阵A分解成3个矩阵的乘积LUD,其中L是下三角矩阵,U是单位上三角矩阵,D是拟对角矩阵(每行只有两个非零元素,前n-1行非零元位于主对角线和最后一列上,第n行非零位于第1列和最后一列上);然后,运用追赶法的思想依次用前代法("追")解出Lu=d的解,回代法("赶")解出Uv=u的解;再利用Dx=v的第一行和最后一行求出未知量Xn,进而回代求解出所有未知量.该方法虽然将系数矩阵分解成3个矩阵的乘积,但计算过程并不复杂,总的算数运算量只有O(14n).小于传统算法的计算量(O(17n)).文章对数值计算的稳定性进行了分析.当矩阵A对角占优且2|ai|≤|bi|时,算法是数值稳定的.数值试验结果与理论分析相吻合.
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| 关 键 词： | 追赶法 循环三对角方程组 矩阵分解 |
A Chasing Method for Solving Cyclic Tridiagonal Equations |
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| LI Wenqiang,MA Min College of Mathematics , Information Science,Henan Normal University,Xinxiang,,Henan Province,China. A Chasing Method for Solving Cyclic Tridiagonal Equations[J]. Science & Technology Review, 2009, 27(14): 69-72 |
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| Authors: | LI Wenqiang MA Min College of Mathematics Information Science Henan Normal University Xinxiang Henan Province China |
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| Affiliation: | LI Wenqiang,MA Min College of Mathematics , Information Science,Henan Normal University,Xinxiang,453007,Henan Province,China |
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| Abstract: | Based on the idea of LU decomposition,the chasing method can be ascribed as the following three steps.Firstly,the coefficient matrix of cyclic tridiagonal equations was decomposed to the multiplication of three matrixes LUD.The matrixes L and U are lower and upper triangular matrix,respectively.While the matrix D is a quasi-diagonal matrix and there are two nonzero entries in the each row of matrix D.Secondly,forward substitution method is used to solve the equation Lu=d,and the backward substitution method... |
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| Keywords: | chasing method cyclic tridiagonal equations matrix decomposition |
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