| H-循环矩阵线性系统求解及其求逆的多项式快速算法 |
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| 引用本文： | 何承源,张坤鹏,马江明.H-循环矩阵线性系统求解及其求逆的多项式快速算法[J].成都电子机械高等专科学校学报,2015(2):54-57. |
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| 作者姓名： | 何承源 张坤鹏 马江明 |
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| 作者单位： | 西华大学理学院,成都,610039 |
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| 基金项目： | 四川省应用基础研究计划“循环矩阵的理论研究及其应用”(2013JY0178) |
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| 摘 要： | 利用多项式理论，给出H-循环矩阵线性系统求解及求逆矩阵的一种快速算法。该快速算法有一个显著特点，求解线性系统时不需要预先知道H-循环矩阵是非奇异还是奇异，得到H-循环矩阵非奇异、唯一解、逆矩阵；或得到H-循环矩阵奇异、有解、特解、通解、自反广义逆矩阵。同时，其逆矩阵及自反广义逆矩阵仍然是H-循环矩阵。
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| 关 键 词： | H-循环矩阵 多项式快速算法 唯一解 通解 逆矩阵 |
The Polynomial Fast Algorithm for Solution of H-circulant Matrix Linear System and Inverse Matrices |
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| HE Chengyuan;ZHANG Kunpeng;MA Jiangming.The Polynomial Fast Algorithm for Solution of H-circulant Matrix Linear System and Inverse Matrices[J].Journal of Chengdu Electromechanical College,2015(2):54-57. |
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| Authors: | HE Chengyuan;ZHANG Kunpeng;MA Jiangming |
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| Affiliation: | HE Chengyuan;ZHANG Kunpeng;MA Jiangming;School of Science,Xihua University; |
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| Abstract: | In this paper, the authors give a fast algorithm for solution of H-circulant matrix linear system and inverse matrices using the theory of polynomials.The fast algorithm has a distinctive feature that solving linear systems does not need to know in advance whether the H-circulant matrix is nonsingular with the result of unique solution and the inverse matrix or the H-circulant matrix is singular having solutions, special solutions, general solution and the reflexive generalized inverse matrix.At the same time, the fast algorithm gives the inverse matrix and reflexive generalized inverse matrix, and the inverse matrix and reflexive generalized inverse matrix are H-circulant matrices. |
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| Keywords: | H-circulant matrix polynomial fast algorithm unique solution general solution inverse matrix |
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