高精度重力加速度的求法

发布时间：2018-03-06 00:14

本文选题：拟合法　切入点：最小二乘法　出处：《解放军理工大学学报(自然科学版)》2016年05期 　论文类型：期刊论文

【摘要】：为了进一步提高单摆测重力加速度的数据拟合精度,基于最小二乘法原理,用线性拟合法分别与指数拟合法、对数拟合法、幂函数拟合法及多项式拟合法结合使用的方法,获得了不同精度的重力加速度拟合值。计算结果表明:采用线性拟合法分别与指数拟合法、对数拟合法、幂函数拟合法结合使用时的数据拟合精度均比直接采用一次线性拟合法低;采用线性拟合法和多项式拟合法结合使用时的数据拟合精度比直接采用一次线性拟合法高;采用线性拟合法和多项式拟合法结合使用时的数据拟合精度随着多项式拟合次数的增加先提高后降低,出现了龙格现象。
[Abstract]:In order to further improve the fitting accuracy of gravity acceleration measured by single pendulum, based on the principle of least square method, the linear fitting method is combined with exponential fitting method, logarithmic fitting method, power function fitting method and polynomial fitting method, respectively. The fitting values of gravity acceleration with different accuracy are obtained. The calculation results show that the linear fitting method is used to match the exponential method and the logarithmic fitting method, respectively. The fitting accuracy of the power function fitting method is lower than that of the direct linear fitting method, and the fitting precision of the power function fitting method is higher than that of the first linear fitting method. With the increase of the degree of polynomial fitting, the precision of data fitting is increased first and then decreased with the combination of linear fitting and polynomial fitting.
【作者单位】：解放军理工大学野战工程学院;
【基金】：国家自然科学基金资助项目(51379213) 国家科技支撑计划资助项目(2014BAB16B05)
【分类号】：O314

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