倾角函数递推公式的误差传递分析

THE ANALYSIS OF ERROR PROPAGATION FOR THE RECURRENT RELATIONS BETWEEN THE INCLINATION FUNCTION

在倾角函数递推关系这个题目上,一些研究者做过工作,如Challe,A(1969),R.H.Googing(1971),J.A.Campbell(1972),G.E.O.Giacaglia(1976)和童付(1979)。最好的结果是由童付获得的,递推关系仅由二个或三个相邻的函数来表达。然而,当倾角较小时,童付的公式存在严重的计算误差传递。本文导出了一个分析公式来估计此种计算误差传递,并在分析计算误差传递机制的基础上,指出可避免计算误差传递的途径,导出的分析公式见文中第(9)式。

On the subject of the recurrent relations between the inclination functions, a number of researchers worked on it, such as Challc, A(1969), R. H. Gooding( 1971), J. A. Campbell (1972), G. E. O. Giacaglia(1976) and Tong Fu(1979). The best result was obtained by Tong Fu. The recurrent relations are expressed to contain only two or three neighbouring functions. However, there is a severe problem on calculating error propagation in Tong Fu' s formulae in the case of relatively small inclination. An analytical formula is deduced in this paper to estimate the calculating error propagation, and a method is suggested to avoid the calculating error propagation on the basis of the analysis of the error propagation process. The deduced formula is the formula (9) in this paper.