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| 求Hankel型线性方程组的一种算法 | |
| 引用本文： | 杨小锋,徐仲,聂玉峰,拓明福. 求Hankel型线性方程组的一种算法[J]. 工程数学学报, 2012, 29(2): 245-252 |
| 作者姓名： | 杨小锋 徐仲 聂玉峰 拓明福 |
| 作者单位： | 1. 西北工业大学应用数学系,西安710072;西北农林科技大学应用数学系,杨凌712100 2. 西北工业大学应用数学系,西安,710072 3. 空军工程大学理学院,西安,710051 |
| 基金项目： | 国家自然科学基金(11071196);陕西省电子信息系统综合集成重点实验室基金(2011ZD08);西北农林科技大学人才基金(01140403)~~ |
| 摘 要： | 本文给出了矩阵为Hankel矩阵的充要条件,由此定义了一种新的矩阵-Hankel型矩阵,说明了Hankel矩阵是Hankel型矩阵的特殊情况.为了降低Hankel型线性方程组的计算量和减小这类算法的误差,利用Hankel型矩阵的位移性质,给出了求Hankel型线性方程组的一种算法.矩阵为Hankel矩阵时,该算法与Gohberg-Kailath-Koltracht算法相比计算量相当,但改进了精度；矩阵为一般Hankel型矩阵时,该算法与Cholesky分解算法相比计算量大为减少,极大改进了精度. |
| 关 键 词： | Hankel矩阵 Hankel型矩阵 快速算法 充要条件 |
An Algorithm for Solving Hankel-type Linear Equations |
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| YANG Xiao-feng , XU Zhong , NIE Yu-feng , TUO Ming-fu. An Algorithm for Solving Hankel-type Linear Equations[J]. Chinese Journal of Engineering Mathematics, 2012, 29(2): 245-252 | |
| Authors: | YANG Xiao-feng XU Zhong NIE Yu-feng TUO Ming-fu |
| Affiliation: | 1-Department of Applied Mathematics,Northwestern Polytechnical University,Xi’an 710072;2-Department of Applied Mathematics,Northwest Agricultural and Forestry University,Yangling 712100;3-College of Science,Air Force Engineering University,Xi’an 710051) |
| Abstract: | In this paper,the necessary and suffcient conditions for Hankel matrices are obtained.We define Hankel-type matrices,and illustrate Hankel matrices are special cases of Hankel-type matrices.In order to decrease the computation amount and reduce the error of linear equations of Hankeltype matrix,an algorithm is presented in term of the displacement structure of Hankel-type matrix.Although the computation amount of new algorithm is same roughly as the Gohberg-Kailath-Koltracht algorithm,more accurate in precision for solving linear equations of Hankel matrix.In general,the algorithm is faster than the Cholesky triangular decomposition algorithm and more accurate in precision for solving system of linear equations of some Hankel-type matrices. |
| Keywords: | Hankel matrix Hankel-type matrix fast algorithm necessary and suffcient condition |
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