边冈逐次分段抛物内插法

B.G.Successive Piecewise Parabolic Interpolation

推广了中国唐代的历算家边冈在其崇玄历中发明的一种逐次分段抛物内插法。通过计算新的插值点上的被插函数与插值函数之差，判断分段效果的好坏，以此确定分段是否仍需进行下去，若是，则此差值便可给出下一轮分段抛物插值函数。并对其收敛性与插值余项的精度估计进行了讨论。

Bian Gang (abbreviated to B.G.),a Chinese calendar-maker in the Tang Dynasty, invented a kind of successive piecewise parabolie interpolation in his Cone Xuan Calendar(892 A.D).Thisalgorithm is in accordance with calculating the difference of values of original and interpolation functions on a new interpolating point to judge the result of piecewise interpolation,and come to adecisionto stop or to continue its procedure.If the difference can not be neolected,the next piecewise parabolic interpolation function is given by the difference immediately.The B.G.interpolation is explained indetail and its convergence and remainder discussed.