| 基于微分方程的散乱数据拟合方法在海水密度问题中的应用 |
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| 引用本文： | 朱亮. 基于微分方程的散乱数据拟合方法在海水密度问题中的应用[J]. 复旦学报(自然科学版), 2009, 48(2) |
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| 作者姓名： | 朱亮 |
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| 作者单位： | 复旦大学数学科学学院,上海,200433 |
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| 摘 要： | 首先提出了一种基于微分方程形式解来拟合数据的方法,其主要思想是通过实验采集的数据点近似地求出这些数据蕴含的目标函数应该满足的微分方程,将它作为目标问题满足的物理模型,然后设法求其形式解来得到基函数,以此为基础拟合散乱数据.接着,利用该方法对国际通用海水密度公式做了一个新的逼近.由实验结果可看出逼近函数不仅在形式上比原公式大大简化,而且还保证了相当的精度(平均误差数量级在10-4kg/m3左右),从而也证明了该方法确实有一定的应用价值.
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| 关 键 词： | 微分方程 数据拟合 国际通用海水密度公式 |
ODE-based Data Fitting Method and Its Application in Equation of State for Seawater |
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| ZHU Liang. ODE-based Data Fitting Method and Its Application in Equation of State for Seawater[J]. Journal of Fudan University(Natural Science), 2009, 48(2) |
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| Authors: | ZHU Liang |
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| Affiliation: | School of Mathematical Sciences;Fudan University;Shanghai 200433;China |
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| Abstract: | An ODE-based(Ordinary Differential Equation based)data fitting method is proposed.By the method the ODEs satisfying the data are found.Then the ODEs to get some base functions which could be used to fit the original data are solved.An application of simplifying the Equation of State for Seawater is then presented.The result shows that the method is effective in form and preserves a high precision of 10-4kg/m3 on average. |
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| Keywords: | differential equation data fitting UNESCO Equation of State for Seawater |
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