| 求线性方程组极小l1范数解的一种算法 |
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| 引用本文： | 姚健康,颜世建.求线性方程组极小l1范数解的一种算法[J].淮阴师范学院学报(自然科学版),2003,2(1):13-18,57. |
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| 作者姓名： | 姚健康 颜世建 |
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| 作者单位： | 1. 河海大学,理学院,南京,210098
2. 南京师范大学,数学与计算机科学,学院,南京,210097 |
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| 摘 要： | 陈中文研究中关于求线性方程组极小l1范数解问题有着较为广泛的应用。本文研究了该问题的最优性条件，给出最优解的充分必要条件。进一步研究了该问题最优解的一种表现形式，提出一个单纯形方法的算法，该算法解决了退化问题，且收敛速度较快，同时给出确定初始基的方法。
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| 关 键 词： | 极小l1范数解 最优性条件 算法 |
| 文章编号： | 1671-6876(2003)01-0013-06 |
An Algorithm for the l1 Norm Solution to the System of Li near Equations |
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| YAO Jian-kang,YAN Shi-jian.An Algorithm for the l1 Norm Solution to the System of Li near Equations[J].Journal of Huaiyin Teachers College(Natrual Science Edition),2003,2(1):13-18,57. |
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| Authors: | YAO Jian-kang YAN Shi-jian |
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| Institution: | YAO Jian-kang1,YAN Shi-jian2 |
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| Abstract: | The problem of solving the minimum l 1 norm solution of an underdetermined system of linear equations is extensively used in many fields. In this paper, we first study the optimal condition, and present a necessary and sufficient condition for the optimal solution of problem. We also give an expression of the optimal solution of problem. Based on these theorems, an algorithm for solving problem, that is a simplex method, is built. The algorithm can solve the problem of the degenerate case, and the convergence rate is fast. |
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| Keywords: | minimum l1 norm solution optimal condition algorithm |
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