| SO(n)中定型矩阵拟合的数值梯度方法 |
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| 引用本文： | 李晓铭,黄建国.SO(n)中定型矩阵拟合的数值梯度方法[J].上海交通大学学报,2005,39(10):1718-1721,1732. |
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| 作者姓名： | 李晓铭 黄建国 |
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| 作者单位： | 上海交通大学,数学系,上海,200240;上海交通大学,数学系,上海,200240 |
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| 基金项目： | 国家自然科学基金资助项目（10371076） |
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| 摘 要： | 提出求解SO（n）中定型矩阵拟合问题导出的约束优化问题的一个数值梯度算法．该方法可视为离散动力系统算法，其最大特点是能始终保持迭代点列满足约束条件．对算法的收敛性和渐近稳定性进行了理论分析，数值试验结果验证了算法的有效性和可靠性．
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| 关 键 词： | 定型拟合问题 数值梯度法 动力系统 收敛性 稳定性 |
| 文章编号： | 1006-2467（2005）10-1718-04 |
| 收稿时间： | 2004-09-18 |
| 修稿时间： | 2004-09-18 |
A Numerical Gradient Algorithm for Finding the Nearest Matrix in SO(n) |
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| LI Xiao-ming,HUANG Jian-guo.A Numerical Gradient Algorithm for Finding the Nearest Matrix in SO(n)[J].Journal of Shanghai Jiaotong University,2005,39(10):1718-1721,1732. |
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| Authors: | LI Xiao-ming HUANG Jian-guo |
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| Institution: | Dept. of Mathematics, Shanghai Jiaotong Univ. , Shanghai 200240, China |
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| Abstract: | A numerical gradient algorithm was proposed to solve a constrained optimization problem arising from a nearestness problem in SO(n),which can be viewed as a discrete dynamical system algorithm.The main advantage of the method is that the iterative sequence always satisfies the constrained condction.The convergence analysis and asymptotical stability analysis were established,and the numerical experiments show the effectiveness and reliability of the algorithm. |
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| Keywords: | nearstness problems numerical gradient algorithms dynamical system convergence stability |
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