高精度重力加速度的求法  

Method of high precision gravity acceleration

作　　者：康少诚 刘华丽[1] 陈徐均[1] KANG Shaocheng LIU Huali CHEN Xujun(College of Field Engineering, PLA Univ. of Sci.＆ Tech., Nanjing 210007,China)

机构地区：[1]解放军理工大学野战工程学院,江苏南京210007

出　　处：《解放军理工大学学报（自然科学版）》2016年第5期413-417,共5页Journal of PLA University of Science and Technology(Natural Science Edition)

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)

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。To further improve the pendulum test data fitting accuracy of the gravity acceleration value, based on the principle of least square method, by the combined use of linear fitting method with index and quasi legitimate, logarithm fitting method, power function quasi legal and polynomial fitting method the different precision of the acceleration of gravity Titted values were obtained. Calculation results show that the precision of data fitting is lower by using the linear quasi legitimate respectively with an exponential, logarithmic, exponential function of the proposed method,compared with a linear fitting; data fitting precision by using the linear quasi legal and polynomial quasi method is higher than directly Using a linear fitting method; and by using the linear fitting method and polynomial fitting method, the fitting accuracy of the data is improved and then decreased with the increase of the number of polynomial fitting, and Runge phenomenon appears.

关 键 词：拟合法 最小二乘法 龙格现象 重力加速度 

分 类 号：O241.2[理学—计算数学]