| 具二次等式约束最小二乘问题的一种极端情形 |
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| 引用本文： | 庄展鹏,刘新国. 具二次等式约束最小二乘问题的一种极端情形[J]. 计算数学, 2012, 34(4): 361-372 |
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| 作者姓名： | 庄展鹏 刘新国 |
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| 作者单位： | 中国海洋大学数学科学学院, 山东青岛 266100 |
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| 基金项目： | 山东省自然科学基金(Y2008A07) |
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| 摘 要： | 本文研究具有二次等式约束的最小二乘问题(LSS): min‖Ax-b‖2 s.t. ‖x‖2=1, 其中A∈Rm×n, b∈Rm, 并假定‖A+b‖2<1.重点关注一个极端情形: ‖A+b‖2≈0. 敏度分析表明,这是一种病态问题. 基于Padé逼近给出了一种迭代解法. 数值算例表明,新方法在速度上较已有方法有优势.
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| 关 键 词： | 最小二乘 病态问题 扰动分析 Padé逼近 |
| 收稿时间： | 2012-07-04; |
AN EXTREME CASE OF LEAST SQUARES PROBLEMS WITH A QUADRATIC EQUALITY CONSTRAIT |
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| Zhuang Zhanpeng,Liu Xinguo. AN EXTREME CASE OF LEAST SQUARES PROBLEMS WITH A QUADRATIC EQUALITY CONSTRAIT[J]. Mathematica Numerica Sinica, 2012, 34(4): 361-372 |
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| Authors: | Zhuang Zhanpeng Liu Xinguo |
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| Affiliation: | School of Mathematical Science, Ocean University of China, QingDao 266100, Shandong, China |
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| Abstract: | This paper studies least squares problem with quadratic equality constraints(LSS): min‖Ax-b‖2 s.t. ‖x‖2=1,where A∈Rm×n, b∈Rm, with the assumption ‖A+b‖2<1. Focus on an extreme case: ‖A+b‖2≈0. A detailed sensitivity analysis shows that this is an illconditioned problem. We present a new iteration method based on Padé approximation. Numerical results demonstrate that the new method is faster than several existing methods. |
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| Keywords: | least squares ill-conditioned problem perturbation analysis Padé approximation |
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