| 关于具二次约束最小二乘问题的敏度分析 |
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| 引用本文： | 刘新国.关于具二次约束最小二乘问题的敏度分析[J].中国海洋大学学报(自然科学版),1996(2). |
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| 作者姓名： | 刘新国 |
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| 基金项目： | 山东省自然科学基金!93A0101 |
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| 摘 要： | 本文系统地研究具二次约束最小二乘问题的敏度分析。首先给出长期方程唯一正根的上界和下界；然后证明割线法用于计算拉格朗日乘子时全局收敛；最后给出解的扰动界。
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| 关 键 词： | LSQ问题 长期方程 敏度分析 乘子 割线法 |
ON THE SENSITIVITY OF THE SOLUTION OF LEAST SQUARES WITH A QUADRATIC CONSTRAINT |
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| Liu Xinguo.ON THE SENSITIVITY OF THE SOLUTION OF LEAST SQUARES WITH A QUADRATIC CONSTRAINT[J].Periodical of Ocean University of China,1996(2). |
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| Authors: | Liu Xinguo |
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| Institution: | Applied Mathematics Department |
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| Abstract: | Least squares with a quadratic constraint (LSQ for short) has a wide range of applications. The solvability and numerical methods have been investigated by Huang Lin, Gander and Elden. In this paper, we deal with the sensitivity analysis of the solution. Firstly, the lower and upper bounds for the unique positive root of the secular equation are given. Then the global convergence of secant iteration for finding the Lagrangian multiplier is proved. Finally, based on some classical results, the perturbation bounds for the solution of LSQ are given. |
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| Keywords: | LSQ problem secular equation sensitivity analysis multiplier secant iteration |
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