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本文对高度异常及垂线偏差的截断误差进行了估计,导出了高阶截断系数的近似表达式。这些截断系数是振幅逐渐衰减的正弦函数,而且其振幅与斯托克司函数在界圆φ_0处的值密切相关。经分析认为,采用莫洛金斯基的最小平方逼近方法,将可使截断误差的数量级大为降低,值得在实际中采用。为了进一步提高截断系数的收敛速度,建议在最小平方逼近的基础上,附加上界圆φ_0处的边界条件,这样将较单纯的逼近为优。为此提出两种实施的方法:利用拉格朗日的条件极值和利用样条函数逼近。
This paper estimates the truncation error of highly anomalous and vertical deviation, and derives the approximate expression of the high-order truncation coefficient. These truncation coefficients are sine functions whose amplitude decays gradually, and their amplitude is closely related to the value of the Stokes function at the bounding circle φ_0. The analysis shows that using the method of least square approximation by Molokinski will reduce the order of magnitude of truncation error significantly and is worthy of being adopted in practice. In order to further improve the convergence rate of the truncation coefficient, it is suggested to add the boundary conditions at the bounding circle φ_0 on the basis of the least squares approximation, so that the simple approximation is better. To do this, we propose two implementation methods: using Lagrange’s conditional extremum and using spline function approximation.