缔和勒让德函数的计算和球谐级数的截断误差分析  

The Computation of Associated Legendre Functions and Truncation Errors of Spherical Harmonic Series

作　　者：刘缵武[1] 张敬伟[2] 刘世晗[2] 王靳辉[1] 

机构地区：[1]解放军信息工程大学理学院,河南郑州450052 [2]河南建筑职业技术学院土木工程系,河南郑州450007

出　　处：《海洋测绘》2012年第3期1-4,共4页Hydrographic Surveying and Charting

基　　金：国家自然科学基金(41074015)

摘　　要：首先就几种新近常用的递推计算超高阶次缔合勒让德函数值的方法进行分析,给出改进后的标准向前列递推法与标准向前列递推法、跨阶次递推法所得球谐级数式的值的相对误差。数值试验表明,改进后的标准向前列递推法与跨阶次递推法所得直到2700阶球谐级数值的相对误差不超过10-13,而标准向前列递推法超过1900阶次时已不可使用。其次估计了不同阶次球谐级数的截断误差,说明如果要获得更高的精度,必须顾及球谐级数的超高阶项。In this paper, some of computing methods of the ultra-high degree and order fully normalized associated Legendre functions （ALFs） are discussed, the relative errors of standard forward column method and recursive method between every order and degree relative to modified standard forward column method are given. And then, truncation errors of value of the spherical harmonic series in different degree and order are calculated. We should take the ultra-high degree and order term values of the spherical harmonic series into account for getting much more numericla precision.

关 键 词：缔合勒让德函数 递推公式 球谐级数 截断误差 

分 类 号：P207[天文地球—测绘科学与技术]