| 非对角占优三对角方程组的一类解法及其数值实验 |
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| 引用本文： | 刘轶中.非对角占优三对角方程组的一类解法及其数值实验[J].华南农业大学学报(社会科学版),2011(1). |
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| 作者姓名： | 刘轶中 |
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| 作者单位： | 贵州大学理学院数学系; |
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| 基金项目： | 贵州省省长优秀科技人才项目(黔省专(2008)19); 贵州大学引进人才科研项目(X065024) |
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| 摘 要： | 针对非对角占优三对角方程组,通过矩阵变换,可将其化为五对角方程组,证明该系数矩阵对称正定,并给出了一组对角占优的充分条件,从而可用多种方法有效地求解。本文用数值实验验证了该算法的有效性。
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| 关 键 词： | 非对角占优 三对角方程组 对称正定 对角占优 数值实验 |
A CLASS OF ALGORITHMS AND NUMERICAL EXPERIMENTS ABOUT THE NONDIAGONALLY DOMINANT TRIDIAGONAL EQUATIONS |
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| LIU Yi-zhong.A CLASS OF ALGORITHMS AND NUMERICAL EXPERIMENTS ABOUT THE NONDIAGONALLY DOMINANT TRIDIAGONAL EQUATIONS[J].Journal of South China Agricultural University:Social Science Edition,2011(1). |
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| Authors: | LIU Yi-zhong |
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| Institution: | LIU Yi-zhong(Department of Mathematics,College of Science,Cuizhou University,Guiyang,Guizhou 550025,China) |
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| Abstract: | In this paper,the nondiagonally dominant tridiagonal equations can be translated into pentadiagonal equations by matrix transformation.Furthermore,the coefficient matrix is proved symmetric positive definite matrix and some sufficient conditions of diagonally dominant is given.The equations can be effectively solved by a variety of methods.In this paper,the effectiveness of the algorithm is illustrated by numerical experiments. |
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| Keywords: | nondiagonally dominant tridiagonal equations symmetric positive definite diagonally dominant numerical experiment |
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