| 首加尾循环线性系统求解的快速算法 |
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| 引用本文： | 田治平.首加尾循环线性系统求解的快速算法[J].山东大学学报(理学版),2011,46(12):96-103. |
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| 作者姓名： | 田治平 |
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| 作者单位： | 山东科技职业学院, 山东 潍坊 261053 |
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| 摘 要： | 利用多项式快速算法,给出了首加尾循环线性系统求解的快速算法。当首加尾循环矩阵非奇异时,该算法求首加尾循环线性系统的惟一解,当首加尾循环矩阵奇异时,该算法求首加尾循环线性系统的特解和通解。最后,利用首加尾循环矩阵与首加尾向后循环矩阵之间的关系,给出了首加尾向后循环线性系统求解的快速算法。
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| 关 键 词： | 首加尾循环线性系统 快速算法 惟一解 通解 |
| 收稿时间： | 2011-06-18 |
Fast algorithm for solving the first plus last circulant linear system |
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| TIAN Zhi-ping.Fast algorithm for solving the first plus last circulant linear system[J].Journal of Shandong University,2011,46(12):96-103. |
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| Authors: | TIAN Zhi-ping |
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| Institution: | Shandong Vocational College of Science and Technology, Weifang 261053, Shandong, China |
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| Abstract: | A fast algorithm for solving the first plus last circulant linear system is presented by the fast algorithm for computing polynomials. When the first plus last circulant matrix is nonsingular, we compute its unique solution. When the first plus last circulant matrix is singular, we compute its special solution and general solution. Finally, a fast algorithm for solving the first plus last retrocirculant linear system is proposed by using the relationship between the first plus last circulant matrix and the first plus last retrocirculant matrix. |
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| Keywords: | the first plus last circulant linear system fast algorithm unique solution general solution |
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